Technology magazine T3 gave the Super Slim model a positive review, stating the console is almost "nostalgic" in the design similarities to the original "fat" model, "While we don’t know whether it will play PS3 games or Blu-ray discs any differently yet, the look and feel of the new PS3 Slim is an obvious homage to the original PS3, minus the considerable excess weight. Immediately we would be concerned about the durability of the top loading tray that feels like it could be yanked straight out off the console, but ultimately it all feels like Sony's nostalgic way of signing off the current generation console in anticipation for the PS4."

What magazine described the Super Slim as "nostalgic"?

What PlayStation 3 model did T3 feel the Super Slim's design was paying homage to?

the original PS3

According to T3, what was the main differentiator between the "fat" PS3 and the Super Slim?

weight

What hardware element did T3 feel might have issues with durability?

the top loading tray

T3 felt Sony was saying goodbye to past models in preparation for what next-generation console?

the PS4

What magazine described the Super Thick as "nostalgic"?

I'm not sure.

What PlayStation 2 model did T3 feel the Super Slim's design was paying homage to?

I'm not sure.

According to T3, what was the main differentiator between the "fat" PS2 and the Super Slim?

I'm not sure.

What hardware element did T2 feel might have issues with durability?

I'm not sure.

T4 felt Sony was saying goodbye to past models in preparation for what next-generation console?

I'm not sure.


Royal assent is sometimes associated with elaborate ceremonies. In the United Kingdom, for instance, the sovereign may appear personally in the House of Lords or may appoint Lords Commissioners, who announce that royal assent has been granted at a ceremony held at the Palace of Westminster. However, royal assent is usually granted less ceremonially by letters patent. In other nations, such as Australia, the governor-general merely signs the bill. In Canada, the governor general may give assent either in person at a ceremony held in the Senate or by a written declaration notifying parliament of his or her agreement to the bill.

When royal assent takes place in the UK, where does the sovereign make an appearance?

House of Lords

Alternatively, when UK Lord Commissioners take the sovereign's place in the ceremony, where does the ceremony take place?

Palace of Westminster

Canadian governor generals can give their assent in person or by which other method?

written declaration

With what is royal assent sometimes associated with?

elaborate ceremonies

Where is a royal assent ceremony held within the United Kingdom?

Palace of Westminster

With what method is royal assent generally granted?

letters patent

How is royal assent granted within Australia?

the governor-general merely signs the bill

What is not associated with elaborate ceremonies?

I'm not sure.

In the US, a sovereign may appear what?

I'm not sure.

Royal assent is usually granted less ceremonially where?

I'm not sure.

In America, the governor-general merely does what to a bill?

I'm not sure.

The sovereign appears personally in the House of Commons in what country?

I'm not sure.


Royal assent is the method by which a country's constitutional monarch (possibly through a delegated official) formally approves an act of that nation's parliament, thus making it a law or letting it be promulgated as law. In the vast majority of contemporary monarchies, this act is considered to be little more than a formality; even in those nations which still permit their ruler to withhold the royal assent (such as the United Kingdom, Norway, and Liechtenstein), the monarch almost never does so, save in a dire political emergency or upon the advice of their government. While the power to withhold royal assent was once exercised often in European monarchies, it is exceedingly rare in the modern, democratic political atmosphere that has developed there since the 18th century.

Royal assent is a process of approving a nation's legislative acts by whom?

constitutional monarch

Which three modern monarchies allow their ruler to withhold royal assent?

United Kingdom, Norway, and Liechtenstein

Since which century have modern political processes forgone royal assent?

What nations allow the withold of the royal assent?

United Kingdom, Norway, and Liechtenstein

Under what circumstances does a monarch typically use the royal assent?

a dire political emergency or upon the advice of their government

Is usage of the royal assent frequent or rare in today's societies?

exceedingly rare

Rigid assent is the process of what?

I'm not sure.

What act is not considered to be little more than a formality?

I'm not sure.

Which power is extremely common in modern democratic atmosphere?

I'm not sure.

Who disapproves of an act of that nation's parliament?

I'm not sure.


Under modern constitutional conventions, the sovereign acts on the advice of his or her ministers. Since these ministers most often maintain the support of parliament and are the ones who obtain the passage of bills, it is highly improbable that they would advise the sovereign to withhold assent. An exception is sometimes stated to be if bills are not passed in good faith, though it is difficult to make an interpretation on what this circumstance might constitute. Hence, in modern practice, royal assent is always granted; a refusal to do so would be appropriate only in an emergency requiring the use of the monarch's reserve powers.

Modern-day sovereigns often acts on the advice of whom?

ministers

In the event that the monarch refuses to give royal assent, what can the monarch make use of?

reserve powers

Whose advice does a sovereign follow?

his or her ministers

Who often maintains parliamentary support and obtains the passage of bills?

ministers

Is it probable, improbable, or impossible that a sovereign would withhold assent?

improbable

Ancient sovereigns acted on the advice of whom?

I'm not sure.

Who stops the passage of bills?

I'm not sure.

Royal assent is never granted in what practice?

I'm not sure.

Whose active powers are required when a royal assent is refused?

I'm not sure.


Originally, legislative power was exercised by the sovereign acting on the advice of the Curia Regis, or Royal Council, in which important magnates and clerics participated and which evolved into parliament. The so-called Model Parliament included bishops, abbots, earls, barons, and two knights from each shire and two burgesses from each borough among its members. In 1265, the Earl of Leicester irregularly called a full parliament without royal authorisation. The body eventually came to be divided into two branches: bishops, abbots, earls, and barons formed the House of Lords, while the shire and borough representatives formed the House of Commons. The King would seek the advice and consent of both houses before making any law. During Henry VI's reign, it became regular practice for the two houses to originate legislation in the form of bills, which would not become law unless the sovereign's assent was obtained, as the sovereign was, and still remains, the enactor of laws. Hence, all acts include the clause "Be it enacted by the Queen's (King's) most Excellent Majesty, by and with the advice and consent of the Lords Spiritual and Temporal, and Commons, in this present Parliament assembled, and by the authority of the same, as follows...". The Parliament Acts 1911 and 1949 provide a second potential preamble if the House of Lords were to be excluded from the process.

What is another name for "Curia Regis"?

Royal Council

Who was it that peculiarly called a full parliament without royal authorization in 1265?

Earl of Leicester

As a result, the bishops, abbots, earls, and barons formed which body of parliament?

House of Lords

Which body did the shire and borough representatives form?

House of Commons

From what did parliament evolve?

Curia Regis, or Royal Council

What positions were contained within the House of Lords?

bishops, abbots, earls, and barons

Which branch of parliament contains shire and borough representatives?

House of Commons

A bill could not become a law without whose assent?

the sovereign

Who is considered the enactor of laws?

the sovereign

The Modern Parliament included whom?

I'm not sure.

In 1665, the Earl of Leicester called a full parliament without what?

I'm not sure.

The Queen would seek the advice of whom before making laws?

I'm not sure.

The two houses in England are the House of Luck and?

I'm not sure.

During Henry VIII's reign, it became common for the two houses to do what?

I'm not sure.


The power of parliament to pass bills was often thwarted by monarchs. Charles I dissolved parliament in 1629, after it passed motions critical of and bills seeking to restrict his arbitrary exercise of power. During the eleven years of personal rule that followed, Charles performed legally dubious actions, such as raising taxes without parliament's approval. After the English Civil War, it was accepted that parliament should be summoned to meet regularly, but it was still commonplace for monarchs to refuse royal assent to bills. In 1678, Charles II withheld his assent from a bill "for preserving the Peace of the Kingdom by raising the Militia, and continuing them in Duty for Two and Forty Days," suggesting that he, not parliament, should control the militia. The last Stuart monarch, Anne, similarly withheld on 11 March 1708, on the advice of her ministers, her assent from a bill for the settling of Militia in Scotland. No monarch has since withheld royal assent on a bill passed by the British parliament.

Which monarch was responsible for dissolving parliament in 1629?

Charles I

What is one action this monarch took that is typically left to the discretion of parliament?

raising taxes

After which event was it decided that parliament should meet on a regular basis?

English Civil War

Like Charles II had previously done, the last Stuart monarch withheld assent. Who was this monarch?

Anne

Which ruler removed parliament in 1629?

Charles I

What did motions attempt to accomplish that prompted Charles I to dissolve parliament in 1629?

restrict his arbitrary exercise of power

When was the last time royal assent was enacted?

11 March 1708

Who was the last monarch to use the royal assent in 1708?

Anne

Under whose advice did Anne withold the royal assent?

her ministers

The power of parliament to pass bills was often supported by whom?

I'm not sure.

Charles I performed legally legitimate what?

I'm not sure.

Who raised taxes with parliament's approval?

I'm not sure.

Who began parliament in 1629?

I'm not sure.

The first Stuart monarch, Anne, did not withhold on what date?

I'm not sure.


During the rule of the succeeding Hanoverian dynasty, power was gradually exercised more by parliament and the government. The first Hanoverian monarch, George I, relied on his ministers to a greater extent than did previous monarchs. Later Hanoverian monarchs attempted to restore royal control over legislation: George III and George IV both openly opposed Catholic Emancipation and asserted that to grant assent to a Catholic emancipation bill would violate the Coronation Oath, which required the sovereign to preserve and protect the established Church of England from Papal domination and would grant rights to individuals who were in league with a foreign power which did not recognise their legitimacy. However, George IV reluctantly granted his assent upon the advice of his ministers. Thus, as the concept of ministerial responsibility has evolved, the power to withhold royal assent has fallen into disuse, both in the United Kingdom and in the other Commonwealth realms.

During whose rule was power transferred more to parliament?

Hanoverian dynasty

Who was the first ruler during this dynasty?

George I

In attempting to take back control, George III and George IV opposed which church movement?

Catholic Emancipation

Which monarch relied on his ministers more than any of his predecessors?

George I

What did George III and George IV both oppose?

Catholic Emancipation

What rule did George III and George IV believe a Catholic emancipation bill would violate?

Coronation Oath

Which monarch granted assent reluctantly under the advise of his ministers?

George IV

George I was the first Hungarian what?

I'm not sure.

Who openly supported Catholic Emancipation?

I'm not sure.

George IV happily granted his assent on whose advice?

I'm not sure.

The power to withhold royal assent has become common where?

I'm not sure.


Royal assent is the final stage in the legislative process for acts of the Scottish parliament. The process is governed by sections 28, 32, and 33 of the Scotland Act 1998. After a bill has been passed, the Presiding Officer of the Scottish Parliament submits it to the monarch for royal assent after a four-week period, during which the Advocate General for Scotland, the Lord Advocate, the Attorney General or the Secretary of State for Scotland may refer the bill to the Supreme Court of the United Kingdom (prior to 1 October 2009, the Judicial Committee of the Privy Council) for review of its legality. Royal assent is signified by letters patent under the Great Seal of Scotland in the following form which is set out in The Scottish Parliament (Letters Patent and Proclamations) Order 1999 (SI 1999/737) and of which notice is published in the London, Edinburgh, and Belfast Gazettes:

In Scotland, who is responsible for submitting a bill for royal assent?

Presiding Officer of the Scottish Parliament

Which three publications are used to signify royal assent?

London, Edinburgh, and Belfast Gazettes

Under which Scotland Act sections is the royal assent governed?

28, 32, and 33

How many weeks pass before the monarch receives a bill from the Presiding Officer?

four-week period

Which entities have the capability to refer a bill to the Supreme Court?

Advocate General for Scotland, the Lord Advocate, the Attorney General or the Secretary of State

For what would a bill be submitted to the Supreme Court of Scotland?

review of its legality

Royal assent is the first stage in what?

I'm not sure.

What process is governed by sections 18, 32, and 33 of the Scotland Act 1998?

I'm not sure.

Before a bill is passed, the Presiding Officer of the Sottish Parliament does what?

I'm not sure.

Royal dissent is signified by what?

I'm not sure.


Measures, which were the means by which the National Assembly for Wales passed legislation between 2006 and 2011, were assented to by the Queen by means of an Order in Council. Section 102 of the Government of Wales Act 2006 required the Clerk to the Assembly to present measures passed by the assembly after a four-week period during which the Counsel General for Wales or the Attorney General could refer the proposed measure to the Supreme Court for a decision as to whether the measure was within the assembly's legislative competence.

What was the name of the method by which Wales passed legislation in the 2000's?

Measures

After a four-week period, who could refer a proposed measure to the Supreme Court?

Counsel General for Wales or the Attorney General

What were "measures" in Wales?

the means by which the National Assembly for Wales passed legislation between 2006 and 2011

During which years were measures used in order to pass legislation in Wales?

2006 and 2011

In Wales, who had the capability of submitting a bill to the Supreme Court?

Counsel General for Wales or the Attorney General

Section 202 of the Government of Wales Act 2006 required what?

I'm not sure.

What was the name by which the National Assembly of America passed legislation?

I'm not sure.

After a three-week period, who could submit a proposed measure to the Supreme Court?

I'm not sure.

What were "measures" in Washington?

I'm not sure.


Instead, the monarch directly grants royal assent by Order in Council. Assent is granted or refused on the advice of the Lord Chancellor. A recent example when assent was refused (or, more correctly, when the Lord Chancellor declined to present the law for assent) was in 2007, concerning reforms to the constitution of the Chief Pleas of Sark. (A revised version of the proposed reforms was subsequently given assent.) In 2011, campaigners against a law that sought to reduce the number of senators in the states of Jersey petitioned the Privy Council to advise the Queen to refuse royal assent. An Order in Council of 13 July 2011 established new rules for the consideration of petitions against granting royal assent.

The sovereign grants assent by which order?

Order in Council

Who advises the sovereign in this decision?

Lord Chancellor

Which recent petition for reforms to the constitution led to assent being refused?

Chief Pleas of Sark

Who advises a bill to be granted or refused?

Lord Chancellor

When was an Order in Counil passed that laid out new rules for consideration of petitions against the royal assent?

13 July 2011

In what year did the Lord Chancellor refuse to present a law  concerning constituational reform for assent?

What was the subject of the bill that the Lord Chancellor refused to present for royal assent in 2007?

reforms to the constitution of the Chief Pleas of Sark

The monarch indirectly grants royal assent how?

I'm not sure.

An Order in Council of 13 July 2001 established what?

I'm not sure.

In 2001, campaigners petitioned whom?

I'm not sure.

The Queen was advised to grant royal assent by campaigners in what year?

I'm not sure.


Royal assent is not sufficient to give legal effect to an Act of Tynwald. By ancient custom, an act did not come into force until it had been promulgated at an open-air sitting of Tynwald, usually held on Tynwald Hill at St John's on St John's Day (24 June), but, since the adoption of the Gregorian calendar in 1753, on 5 July (or on the following Monday if 5 July is a Saturday or Sunday). Promulgation originally consisted of the reading of the Act in English and Manx; but, after 1865 the reading of the title of the act and a summary of each section were sufficient. This was reduced in 1895 to the titles and a memorandum of the object and purport of the act, and, since 1988, only the short title and a summary of the long title have been read.

Under ancient custom, an Act of Tynwald didn't go into effect until decreed at which location?

Tynwald Hill at St John's

Promulgation of an Act of Tynwald originally consisted of reading it in English and which other language?

Manx

Nowadays, only the short title and what else are read?

summary of the long title

How much of the proposed act must be currently read aloud on St John's Day?

only the short title and a summary of the long title

On what day does St John's Day occur?

(24 June)

Where is the open-air sitting of Tynwald usually held?

Tynwald Hill at St John's

Royal assent gives legal effect to an Act of what?

I'm not sure.

What was reduced in 1995?

I'm not sure.

Since what year has only the short title been read?

I'm not sure.

The adoption of the Greek calendar was made in what year?

I'm not sure.


Since 1993, the Sodor and Man Diocesan Synod has had power to enact measures making provision "with respect to any matter concerning the Church of England in the Island". If approved by Tynwald, a measure "shall have the force and effect of an Act of Tynwald upon the Royal Assent thereto being announced to Tynwald". Between 1979 and 1993, the Synod had similar powers, but limited to the extension to the Isle of Man of measures of the General Synod. Before 1994, royal assent was granted by Order in Council, as for a bill, but the power to grant royal assent to measures has now been delegated to the lieutenant governor. A Measure does not require promulgation.

Since 1993, which body has had power to enact measures?

Sodor and Man Diocesan Synod

This body makes provisions in respect to matters concerning whom?

Church of England in the Island

Up until 1994, royal assent was given by whom?

Order in Council

Which position now has the power to grant royal assent?

lieutenant governor

Before what year was royal assent approved by Order in Council?

Who currently holds the power to grant royal assent to measures?

the lieutenant governor

During which years did the Synod have power to enact measures?

Between 1979 and 1993

Since 1983, who has had power to enact measures?

I'm not sure.

Before 1994, royal dissent was granted by whom?

I'm not sure.

Currently, royal dissent has been delegated to whom?

I'm not sure.

What requires promulgation?

I'm not sure.


If the Governor General of Canada is unable to give assent, it can be done by either the Deputy of the Governor General of Canada—the Chief Justice of Canada—or another justice of the Supreme Court of Canada. It is not actually necessary for the governor general to sign a bill passed by a legislature, the signature being merely an attestation. In each case, the parliament must be apprised of the granting of assent before the bill is considered to have become law. Two methods are available: the sovereign's representatives may grant assent in the presence of both houses of parliament; alternatively, each house may be notified separately, usually by the speaker of that house. However, though both houses must be notified on the same day, notice to the House of Commons while it is not in session may be given by way of publishing a special issue of the Journals of the House of Commons, whereas the Senate must be sitting and the governor general's letter read aloud by the speaker.

In the Canadian federal government, who is typically responsible for deciding wether to give assent?

the Governor General of Canada

Which positions from the Canadian Supreme Court may also give assent if need be?

Chief Justice of Canada—or another justice

Who has the capability of granting assent if the Governer General of Canada cannot?

the Deputy of the Governor General of Canada—the Chief Justice of Canada—or another justice of the Supreme Court of Canada

How many methods are available to grant assent in Canada?

Two

If each house of parliament is notified seperately, what regulation applies?

both houses must be notified on the same day

How can the House of Commons be notified of assent if it is not in session?

publishing a special issue of the Journals of the House of Commons

In contrast to the House of Commons, how must the Senate be notified of assent?

governor general's letter read aloud by the speaker

It is necessary for the governor general to sign what?

I'm not sure.

Parliament is never apprised of what?

I'm not sure.

Both what must be notified on separate days?

I'm not sure.

The Journals of the House of Lords may publish a special what?

I'm not sure.


While royal assent has not been withheld in the United Kingdom since 1708, it has often been withheld in British colonies and former colonies by governors acting on royal instructions. In the United States Declaration of Independence, colonists complained that George III "has refused his Assent to Laws, the most wholesome and necessary for the public good [and] has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them." Even after colonies such as Canada, Australia, New Zealand, the Union of South Africa, and Newfoundland were granted responsible government, the British government continued to sometimes advise governors-general on the granting of assent; assent was also occasionally reserved to allow the British government to examine a bill before advising the governor-general.

Which year was royal assent last withheld in the UK?

The United States Declaration of Independence mentions which British monarch?

George III

What did the American colonies accuse the monarch of?

refused his Assent to Laws

In what year was royal assent last witheld in the UK?

Who continued to advise governors-general of granting of assent, even after their colonies had responsible government?

the British government

To whom did the British government occasionally still advice on the royal assent, although they had their own responsible governments?

colonies such as Canada, Australia, New Zealand, the Union of South Africa, and Newfoundland

Royal assent has been withheld in the UK since what year?

I'm not sure.

US colonists complained the George II had refused what?

I'm not sure.

Which countries were not granted a responsible government?

I'm not sure.

Assent is never reserved to allow the British government to examine what?

I'm not sure.


In Australia, a technical issue arose with the royal assent in both 1976 and 2001. In 1976, a bill originating in the House of Representatives was mistakenly submitted to the Governor-General and assented to. However, it was later discovered that it had not been passed by each house. The error arose because two bills of the same title had originated from the house. The Governor-General revoked the first assent, before assenting to the bill which had actually passed. The same procedure was followed to correct a similar error which arose in 2001.

The bill from the Australian House of Representatives was mistakenly sent and assented to by whom in 1976?

Governor-General

Why did this occur?

two bills of the same title had originated from the house

What did the Governor-General do with the first assent?

revoked the first assent

This same procedure was more recently done to fix a similar error in which year?

What was the reason a bill was accidentally assented in 1976?

two bills of the same title had originated from the house

After an accidental assention of a bill with same name in 1976, when did a similar mistaken assention occur in Australia?

What protocol was not followed in 1976 when a bill was mistakenly assented?

it had not been passed by each house

How was the case of two bills mistakenly assented corrected both in 1796 and 2001?

The Governor-General revoked the first assent, before assenting to the bill which had actually passed

In America, a technical issue arose with what in 1976 and 2001?

I'm not sure.

A bill from the House of Lords was mistakenly submitted in what year?

I'm not sure.

Three bills with the same title were submitted in what year?

I'm not sure.

Who revoked the second assent?

I'm not sure.


Special procedures apply to legislation passed by Tynwald, the legislature of the Isle of Man. Before the lordship of the Island was purchased by the British Crown in 1765 (the Revestment), the assent of the Lord of Mann to a bill was signified by letter to the governor. After 1765, royal assent was at first signified by letter from the Secretary of State to the governor; but, during the British Regency, the practice began of granting royal assent by Order in Council, which continues to this day, though limited to exceptional cases since 1981.

What term refers to the legislature of the Isle of man?

Tynwald

In what year was lordship of the Isle of Man purchased?

What does the term the Revestment refer to?

lordship of the Island was purchased by the British Crown in 1765

How is royal assent currently granted in the Isle of Man?

Order in Council

Previous to the Order in Council method, how was royal assent passed previously within the Isle of Man?

by letter from the Secretary of State to the governor

What is the legislature of the Isle of Women?

I'm not sure.

The lordship of the Isle of Man was purchased by America in what year?

I'm not sure.

After 1665, royal assent was signified how?

I'm not sure.

Who signified the letter of royal assent in America after 1765?

I'm not sure.


In Commonwealth realms other than the UK, royal assent is granted or withheld either by the realm's sovereign or, more frequently, by the representative of the sovereign, the governor-general. In federated realms, assent in each state, province, or territory is granted or withheld by the representatives of the sovereign. In Australia, this is the governors of the states, administrators of the territories, or the governor-general in the Australian Capital Territory. For Canada, this is the lieutenant governors of the provinces. A lieutenant governor may defer assent to the governor general, and the governor general may defer assent to federal bills to the sovereign.

In Commonwealth realms, who is the representative of the sovereign?

the governor-general

Who grants royal assent in Canada?

lieutenant governors of the provinces

In Canada, who is authorized to defer assent and to whom?

A lieutenant governor may defer assent to the governor general, and the governor general may defer assent to federal bills to the sovereign.

Who grants the royal assent in Commonwealth nations other than the UK?

by the realm's sovereign or, more frequently, by the representative of the sovereign

The representative of the sovereign in America is whom?

I'm not sure.

The representative of the sovereign in Chile is whom?

I'm not sure.

The realm's sovereign grants or withholds regal what?

I'm not sure.

A vice lieutenant governor may defer what?

I'm not sure.


Since the Balfour Declaration of 1926 and the Statute of Westminster 1931, the all Commonwealth realms have been sovereign kingdoms, the monarch and governors-general acting solely on the advice of the local ministers who generally maintain the support of the legislature and are the ones who secure the passage of bills. They, therefore, are unlikely to advise the sovereign or his or her representative to withhold assent. The power to withhold the royal assent was exercised by Alberta's lieutenant governor, John C. Bowen, in 1937, in respect of three bills passed in the legislature dominated by William Aberhart's Social Credit party. Two bills sought to put banks under the authority of the province, thereby interfering with the federal government's powers. The third, the Accurate News and Information Bill, purported to force newspapers to print government rebuttals to stories to which the provincial cabinet objected. The unconstitutionality of all three bills was later confirmed by the Supreme Court of Canada and by the Judicial Committee of the Privy Council.

What two documents declared all Commonwealth realms as sovereign kingdoms?

Balfour Declaration of 1926 and the Statute of Westminster 1931

Who exercised the power to withold royal assent in Alberta in 1937?

John C. Bowen

What the did Accurate News and Information Bill hope to accomplish?

force newspapers to print government rebuttals to stories to which the provincial cabinet objected

Who decided the unconstitutionality of three bills brought forth by the Social Credit party?

Supreme Court of Canada and by the Judicial Committee of the Privy Council.

No Commonwealth realms are sovereign what?

I'm not sure.

The Barker Declaration came into being in what year?

I'm not sure.

The Declaration of Westminster came into being in what year?

I'm not sure.

How many bills sought to put the provinces under the authority of the banks?

I'm not sure.


In the United Kingdom, a bill is presented for royal assent after it has passed all the required stages in both the House of Commons and the House of Lords. Under the Parliament Acts 1911 and 1949, the House of Commons may, under certain circumstances, direct that a bill be presented for assent despite lack of passage by the House of Lords. Officially, assent is granted by the sovereign or by Lords Commissioners authorised to act by letters patent. It may be granted in parliament or outside parliament; in the latter case, each house must be separately notified before the bill takes effect.

Which Houses in the UK must approve a bill before it is assented?

House of Commons and the House of Lords

Which Parliamentary Acts allow a bill to be presented for assent even after the House of Lords has refused it?

Parliament Acts 1911 and 1949

Who can be authorized to grant assent by letters patent?

the sovereign or by Lords Commissioners

What is presented for royal assent in the US?

I'm not sure.

Under the Parliament Acts of 1917 and 1949, the House of Commons may do what?

I'm not sure.

Unofficially, assent is granted how?

I'm not sure.

Each house must be notified jointly before what?

I'm not sure.


The Clerk of the Parliaments, an official of the House of Lords, traditionally states a formula in Anglo-Norman Law French, indicating the sovereign's decision. The granting of royal assent to a supply bill is indicated with the words "La Reyne remercie ses bons sujets, accepte leur benevolence, et ainsi le veult", translated as "The Queen thanks her good subjects, accepts their bounty, and wills it so." For other public or private bills, the formula is simply "La Reyne le veult" ("the Queen wills it"). For personal bills, the phrase is "Soit fait comme il est désiré" ("let it be as it is desired"). The appropriate formula for withholding assent is the euphemistic "La Reyne s'avisera" ("the Queen will consider it"). When the sovereign is male, Le Roy is substituted for La Reyne.

In what language does the Clerk of the Parliaments announce Parliament's decision?

Anglo-Norman Law French

What words in Anglo-Norman Law French announce a granted assent?

"La Reyne remercie ses bons sujets, accepte leur benevolence, et ainsi le veult"

What is the shortened version of the notification of assent?

"La Reyne le veult"

What phrase is used to announce a withheld assent?

"La Reyne s'avisera"

Who is an official of the House of Commons?

I'm not sure.

A formula in Anglo-Norman Law Greek indicates what?

I'm not sure.

The inappropriate formula for withholding assent is what?

I'm not sure.

The translation for "the Queen will not consider it" is what?

I'm not sure.


Before the reign of Henry VIII, the sovereign always granted his or her assent in person. The sovereign, wearing the Imperial State Crown, would be seated on the throne in the Lords chamber, surrounded by heralds and members of the royal court—a scene that nowadays is repeated only at the annual State Opening of Parliament. The Commons, led by their speaker, would listen from the Bar of the Lords, just outside the chamber. The Clerk of the Parliaments presented the bills awaiting assent to the monarch, save that supply bills were traditionally brought up by the speaker. The Clerk of the Crown, standing on the sovereign's right, then read aloud the titles of the bills (in earlier times, the entire text of the bills). The Clerk of the Parliaments, standing on the sovereign's left, responded by stating the appropriate Norman French formula.

When assention was formally granted in person, who read the titles of the bills?

The Clerk of the Crown

What job did the Clerk of the Parliaments have during assention notifications?

stating the appropriate Norman French formula

Before whose reign was assent always granted in person?

Henry VIII

Nowadays, when is the only time a formal assention ceremony occurs?

the annual State Opening of Parliament

On which side of the soverign does the Clerk of the Crown stand?

right

Before the reign of Henry I, the sovereign granted assent how?

I'm not sure.

Who would wear the Imperial State Tiara?

I'm not sure.

Who would sit on the throne in the Queens chamber?

I'm not sure.

Who would stand in front of the sovereign and read the titles of the bills?

I'm not sure.


A new device for granting assent was created during the reign of King Henry VIII. In 1542, Henry sought to execute his fifth wife, Catherine Howard, whom he accused of committing adultery; the execution was to be authorised not after a trial but by a bill of attainder, to which he would have to personally assent after listening to the entire text. Henry decided that "the repetition of so grievous a Story and the recital of so infamous a crime" in his presence "might reopen a Wound already closing in the Royal Bosom". Therefore, parliament inserted a clause into the Act of Attainder, providing that assent granted by Commissioners "is and ever was and ever shall be, as good" as assent granted by the sovereign personally. The procedure was used only five times during the 16th century, but more often during the 17th and 18th centuries, especially when George III's health began to deteriorate. Queen Victoria became the last monarch to personally grant assent in 1854.

Why did Henry VIII wish to execute his fifth wife?

committing adultery

What was Henry VIII trying to avoid by creating a new procedure for granting assent?

listening to the entire text

How many times in the 16th century was assent granted by Commissioners?

five

Who was the last monarch to grant assent personally?

Queen Victoria

King Henry VIII sought to execute his sixth wife in what year?

I'm not sure.

Catherine Howard was the sixth wife of whom?

I'm not sure.

A clause was taken out of the Act of what?

I'm not sure.

Queen Victoria was the last what to grant assent in 1954?

I'm not sure.


When granting assent by commission, the sovereign authorises three or more (normally five) lords who are Privy Counsellors to grant assent in his or her name. The Lords Commissioners, as the monarch's representatives are known, wear scarlet parliamentary robes and sit on a bench between the throne and the Woolsack. The Lords Reading Clerk reads the commission aloud; the senior commissioner then states, "My Lords, in obedience to Her Majesty's Commands, and by virtue of the Commission which has been now read, We do declare and notify to you, the Lords Spiritual and Temporal and Commons in Parliament assembled, that Her Majesty has given Her Royal Assent to the several Acts in the Commission mentioned."

How many lords are usually present during assent by Commissioner?

five

What do the Lords Commissioners wear to a ceremony of assent?

scarlet parliamentary robes

Which commissioner reads the formal closing statement to the assention ceremony?

the senior

Which position reads the commisssion aloud during tthe ceremony?

The Lords Reading Clerk

Who reads the commission silently?

I'm not sure.

The junior commissioner makes a statement after whom?

I'm not sure.

The king's representatives are know as whom?

I'm not sure.

How many commoners are involved in granting assent by commission?

I'm not sure.

Who wears blue parliamentary robes?

I'm not sure.


During the 1960s, the ceremony of assenting by commission was discontinued and is now only employed once a year, at the end of the annual parliamentary session. In 1960, the Gentleman Usher of the Black Rod arrived to summon the House of Commons during a heated debate and several members protested against the disruption by refusing to attend the ceremony. The debacle was repeated in 1965; this time, when the Speaker left the chair to go to the House of Lords, some members continued to make speeches. As a result, the Royal Assent Act 1967 was passed, creating an additional form for the granting of royal assent. As the attorney-general explained, "there has been a good deal of resentment not only at the loss of Parliamentary time that has been involved but at the breaking of the thread of a possibly eloquent speech and the disruption of a debate that may be caused." The granting of assent by the monarch in person, or by commission, is still possible, but this third form is used on a day-to-day basis.

During which decade was assention by commission discontinued?

the 1960s

When does assention by commission occur today?

once a year, at the end of the annual parliamentary session

In whatear did several members refuse to attend the assention ceremony after a heated debate?

What was passed in reference to the discord in 1960 and 1965 during assention cremonies?

Royal Assent Act 1967

The ceremony of assenting by commission was continued in what decade?

I'm not sure.

The German Usher of the Black Rod summoned whom in 1960?

I'm not sure.

The Royal Assent Act 1968 was passed why?

I'm not sure.

The granting of what by the monarch in person is no longer possible?

I'm not sure.


Under the Royal Assent Act 1967, royal assent can be granted by the sovereign in writing, by means of letters patent, that are presented to the presiding officer of each house of parliament. Then, the presiding officer makes a formal, but simple statement to the house, acquainting each house that royal assent has been granted to the acts mentioned. Thus, unlike the granting of royal assent by the monarch in person or by Royal Commissioners, the method created by the Royal Assent Act 1967 does not require both houses to meet jointly for the purpose of receiving the notice of royal assent. The standard text of the letters patent is set out in The Crown Office (Forms and Proclamations Rules) Order 1992, with minor amendments in 2000. In practice this remains the standard method, a fact that is belied by the wording of the letters patent for the appointment of the Royal Commissioners and by the wording of the letters patent for the granting of royal assent in writing under the 1967 Act ("... And forasmuch as We cannot at this time be present in the Higher House of Our said Parliament being the accustomed place for giving Our Royal Assent...").

What is unique about the method used for assention allowed by the Royal Assent Act 1967?

does not require both houses to meet jointly

How is assent granted under the Royal Assent Act 1967?

by the sovereign in writing, by means of letters patent, that are presented to the presiding officer of each house of parliament

Which document formats the letters patent?

The Crown Office (Forms and Proclamations Rules) Order 1992

In which year were minor amendments made to the Crown Office Order?

In the Royal Assent Act 1968, royal assent can be granted how?

I'm not sure.

The presiding officer makes an informal statement to whom?

I'm not sure.

Which method requires both houses to meet jointly?

I'm not sure.

Which act allows the sovereign to grant assent verbally?

I'm not sure.


When the act is assented to by the sovereign in person, or by empowered Royal Commissioners, royal assent is considered given at the moment when the assent is declared in the presence of both houses jointly assembled. When the procedure created by the Royal Assent Act 1967 is followed, assent is considered granted when the presiding officers of both houses, having received the letters patent from the king or queen signifying the assent, have notified their respective house of the grant of royal assent. Thus, if each presiding officer makes the announcement at a different time (for instance because one house is not sitting on a certain date), assent is regarded as effective when the second announcement is made. This is important because, under British Law, unless there is any provision to the contrary, an act takes effect on the date on which it receives royal assent and that date is not regarded as being the date when the letters patent are signed, or when they are delivered to the presiding officers of each house, but the date on which both houses have been formally acquainted of the assent.

When assent is granted in person, when is it formally considered final?

when the assent is declared in the presence of both houses jointly assembled

An assent is considered granted when applying the Royal Assent Act 1967 when both presiding officers have done what?

notified their respective house of the grant of royal assent

When is assent effective if the presiding officers inform their houses at different times?

when the second announcement is made

Royal Assent is considered not given at what moment?

I'm not sure.

When the Royal Assent Act 1967 is not followed, assent is considered granted when?

I'm not sure.

Assent is regarded as ineffective when?

I'm not sure.

Under American law, an act takes effect when?

I'm not sure.


Independently of the method used to signify royal assent, it is the responsibility of the Clerk of the Parliaments, once the assent has been duly notified to both houses, not only to endorse the act in the name of the monarch with the formal Norman French formula, but to certify that assent has been granted. The clerk signs one authentic copy of the bill and inserts the date (in English) on which the assent was notified to the two houses after the title of the act. When an act is published, the signature of the clerk is omitted, as is the Norman French formula, should the endorsement have been made in writing. However, the date on which the assent was notified is printed in brackets.

Whose responsibility is it to assure that assent has been granted?

Clerk of the Parliaments

What is omitted when an act is published?

signature of the clerk is omitted, as is the Norman French formula

Who writes the formal Norman French formula on passed acts?

Clerk of the Parliaments

It is the responsibility of the Clerk of the Lords to endorse what?

I'm not sure.

The German French formula is used to endorse what?

I'm not sure.

The clerk signs two copies of what?

I'm not sure.

The date is inserted in French on what?

I'm not sure.


In Australia, the formal ceremony of granting assent in parliament has not been regularly used since the early 20th century. Now, the bill is sent to the governor-general's residence by the house in which it originated. The governor-general then signs the bill, sending messages to the President of the Senate and the Speaker of the House of Representatives, who notify their respective houses of the governor-general's action. A similar practice is followed in New Zealand, where the governor-general has not personally granted the Royal Assent in parliament since 1875.

In what year did the New Zealand governor-general last personally grant the royal assent in parliament?

Which country has not used the formal assention ceremony since the early 20th century?

Australia

Who are the leaders of each house given the responsibility of informing their group of the governor-generals actions?

President of the Senate and the Speaker of the House of Representatives

What has not been used regularly since the early 20th century in America?

I'm not sure.

In New Zealland, the governor-general has personally granted the Royal Assent since what year?

I'm not sure.

What type of ceremony is commonly used to grant assent in Australia?

I'm not sure.

The governor-general of Australia sends messages to the Vice President of the Senate and whom to grant assent?

I'm not sure.


In Canada, the traditional ceremony for granting assent in parliament was regularly used until the 21st century, long after it had been discontinued in the United Kingdom and other Commonwealth realms. One result, conceived as part of a string of royal duties intended to demonstrate Canada's status as an independent kingdom, was that King George VI personally assented to nine bills of the Canadian parliament during the 1939 royal tour of Canada—85 years after his great-grandmother, Queen Victoria, had last granted royal assent personally in the United Kingdom. Under the Royal Assent Act 2002, however, the alternative practice of granting assent in writing, with each house being notified separately ( the Speaker of the Senate or a representative reads to the senators the letters from the governor general regarding the written declaration of Royal Assent), was brought into force. As the act also provides, royal assent is to be signified—by the governor general, or, more often, by a deputy, usually a Justice of the Supreme Court, at least twice each calendar year: for the first appropriation measure and for at least one other act, usually the first non-appropriation measure passed. However, the act provides that a grant of royal assent is not rendered invalid by a failure to employ the traditional ceremony where required.

When did Canada finally cease to use the traditional ceremony for granting assent as regular practice?

the 21st century

Why was King George VI's personal assent in 1939 noteworthy?

85 years after his great-grandmother, Queen Victoria, had last granted royal assent personally

With what bill in Canada did granting assent by writing become effective?

Royal Assent Act 2002

In Chile, the ceremony for granting assent was used until what century?

I'm not sure.

What king assented to nineteen bills of the Canadian parliament during the 1939 royal tour?

I'm not sure.

Who was King George VI's grandmother?

I'm not sure.

A grant of royal assent is rendered invalid by what?

I'm not sure.


The Royal Assent ceremony takes place in the Senate, as the sovereign is traditionally barred from the House of Commons. On the day of the event, the Speaker of the Senate will read to the chamber a notice from the secretary to the governor general indicating when the viceroy or a deputy thereof will arrive. The Senate thereafter cannot adjourn until after the ceremony. The speaker moves to sit beside the throne, the Mace Bearer, with mace in hand, stands adjacent to him or her, and the governor general enters to take the speaker's chair. The Usher of the Black Rod is then commanded by the speaker to summon the Members of Parliament, who follow Black Rod back to the Senate, the Sergeant-at-Arms carrying the mace of the House of Commons. In the Senate, those from the commons stand behind the bar, while Black Rod proceeds to stand next to the governor general, who then nods his or her head to signify Royal Assent to the presented bills (which do not include appropriations bills). Once the list of bills is complete, the Clerk of the Senate states: "in Her Majesty's name, His [or Her] Excellency the Governor General [or the deputy] doth assent to these bills." If there are any appropriation bills to receive Royal Assent, the Speaker of the House of Commons will read their titles and the Senate clerk repeats them to the governor general, who nods his or her head to communicate Royal Assent. When these bills have all been assented to, the Clerk of the Senate recites "in Her Majesty's name, His [or Her] Excellency the Governor General [or the deputy] thanks her loyal subjects, accepts their benevolence and assents to these bills. The governor general or his or her deputy then depart parliament.

From where is the sovereign typically forbidden?

House of Commons

Whose job is it to release parliament after the ceremony?

The governor general or his or her deputy

Who reads the formal statement after the list of bills has been finished?

Clerk of the Senate

Which position nods their head to signify assention?

governor general

What ceremony takes place in the House?

I'm not sure.

On the day of the event, the President of the Senate reads to whom?

I'm not sure.

On the day of the event, the President of the Senate reads what?

I'm not sure.

Who follows Black Rod back to the Senate?

I'm not sure.


In Belgium, the sanction royale has the same legal effect as royal assent; the Belgian constitution requires a theoretically possible refusal of royal sanction to be countersigned—as any other act of the monarch—by a minister responsible before the House of Representatives. The monarch promulgates the law, meaning that he or she formally orders that the law be officially published and executed. In 1990, when King Baudouin advised his cabinet he could not, in conscience, sign a bill decriminalising abortion (a refusal patently not covered by a responsible minister), the Council of Ministers, at the King's own request, declared Baudouin incapable of exercising his powers. In accordance with the Belgian constitution, upon the declaration of the sovereign's incapacity, the Council of Ministers assumed the powers of the head of state until parliament could rule on the King's incapacity and appoint a regent. The bill was then assented to by all members of the Council of Ministers "on behalf of the Belgian People". In a joint meeting, both houses of parliament declared the King capable of exercising his powers again the next day.

What is royal assent called in Belgium?

sanction royale

Who declared the monarch incapable of acting upon an abortion decriminalization bill in 1990?

Council of Ministers

Which King refused to sign an abortion decriminalization bill in 1990?

King Baudouin

Who declared the King capable of excersizing power again after a brief lapse in 1990?

both houses of parliament

In Bulgaria, what has the same effect as royal assent?

I'm not sure.

King Bedoin refused to sign a bill in what year?

I'm not sure.

Both houses declared King Baudouin incapable of exercising his powers in what type of meeting?

I'm not sure.

King Baudouin signed a bill criminalizing abortion in what year?

I'm not sure.


The constitution of Jordan grants its monarch the right to withhold assent to laws passed by its parliament. Article 93 of that document gives the Jordanian sovereign six months to sign or veto any legislation sent to him from the National Assembly; if he vetoes it within that timeframe, the assembly may override his veto by a two-thirds vote of both houses; otherwise, the law does not go into effect (but it may be reconsidered in the next session of the assembly). If the monarch fails to act within six months of the bill being presented to him, it becomes law without his signature.

How much time does a Jordinian leader have to sign or veto legislation?

six months

What majority is required to override a veto from the soverign?

two-thirds

What happens if the soverign doesn't sign the bill within the six-month time frame?

, it becomes law without his signature

The constitution of Jordan does not grant the monarch the right to do what?

I'm not sure.

Article 83 gives the Jordanian sovereign how much time to signor veto legislation?

I'm not sure.

What kind of vote from either house is required to override the Jordanian sovereign?

I'm not sure.

If the monarch fails to act within four months what happens?

I'm not sure.


After the House of Representatives has debated the law, it either approves it and sends it to the Senate with the text "The Second Chamber of the States General sends the following approved proposal of law to the First Chamber", or it rejects it and returns it to the government with the text "The Second Chamber of the States General has rejected the accompanying proposal of law." If the upper house then approves the law, it sends it back to the government with the text "To the King, The States General have accepted the proposal of law as it is offered here."

What text is written and sent to the Senate if the House approves of a law?

"The Second Chamber of the States General sends the following approved proposal of law to the First Chamber"

What text is written and sent back to the government if a bill is rejected?

The Second Chamber of the States General has rejected the accompanying proposal of law."

If the Senate approves the law after receiving it from the House, what is written and sent to the government?

"To the King, The States General have accepted the proposal of law as it is offered here."

What is one thing that could happen after the House of Lords debates the law?

I'm not sure.

If the lower house approves the law, what happens?

I'm not sure.

What text is sent to the House of Representatives if a law is approved?

I'm not sure.

What text is sent to the House of Representatives if a law is not approved?

I'm not sure.


The government, consisting of the monarch and the ministers, will then usually approve the proposal and the sovereign and one of the ministers signs the proposal with the addition of an enacting clause, thereafter notifying the States General that "The King assents to the proposal." It has happened in exceptional circumstances that the government does not approve a law that has been passed in parliament. In such a case, neither the monarch nor a minister will sign the bill, notifying the States General that "The King will keep the proposal under advisement." A law that has received royal assent will be published in the State Magazine, with the original being kept in the archives of the King's Offices.

Where are laws published after receiving assent?

the State Magazine

Where is the original law text stored?

in the archives of the King's Offices

What happens in the rare case the government doesn't approve of a law that has passed both houses?

neither the monarch nor a minister will sign the bill, notifying the States General that "The King will keep the proposal under advisement."

The sovereign and two what signs the proposal?

I'm not sure.

The enabling clause is added to what?

I'm not sure.

In what case will the monarch but not the minister sign the bill?

I'm not sure.

A law that has not received royal assent will be published where?

I'm not sure.


Articles 77–79 of the Norwegian Constitution specifically grant the monarch of Norway the right to withhold royal assent from any bill passed by the Storting. Should the sovereign ever choose to exercise this privilege, Article 79 provides a means by which his veto may be over-ridden: "If a Bill has been passed unaltered by two sessions of the Storting, constituted after two separate successive elections and separated from each other by at least two intervening sessions of the Storting, without a divergent Bill having been passed by any Storting in the period between the first and last adoption, and it is then submitted to the King with a petition that His Majesty shall not refuse his assent to a Bill which, after the most mature deliberation, the Storting considers to be beneficial, it shall become law even if the Royal Assent is not accorded before the Storting goes into recess."

Which articles in the Norwegian Constitution allow the monarch to reject a bill that has been passed through the Sorting?

Articles 77–79

Which article in the Norweigan Constitution provides a way to override a monarch's veto?

Article 79

How many elections are required to assend a bill that the monarch has vetoed?

two

Articles 67-69 of the Norwegian Constitution grant what?

I'm not sure.

Which article provides a means by which a sovereigns' veto may not be over-ridden?

I'm not sure.

Which articles of the Norwegian Constitution do not grant the monarch the right to withhold royal assent?

I'm not sure.

The monarch of New England can withhold royal assent according to which articles?

I'm not sure.


Title IV of the 1978 Spanish constitution invests the Consentimiento Real (Royal Assent) and promulgation (publication) of laws with the monarch of Spain, while Title III, The Cortes Generales, Chapter 2, Drafting of Bills, outlines the method by which bills are passed. According to Article 91, within fifteen days of passage of a bill by the Cortes Generales, the sovereign shall give his or her assent and publish the new law. Article 92 invests the monarch with the right to call for a referendum, on the advice of the president of the government (commonly referred to in English as the prime minister) and the authorisation of the cortes.

Which article in the Spanish constitution gives the monarch the right to ask for a referendum?

Article 92

Which article specifies the number of days available to the monarch to provide a signature on an assended bill?

Article 91

In the 1978 Spanish constitution, which title describes how bills are passed?

Title III, The Cortes Generales

What chapter in the Spanish constitution describes how bills are to be passed?

Chapter 2, Drafting of Bills

Which title outlines the method by which bills are not passed?

I'm not sure.

Which title does not invest the royal assent and publication of laws with the monarch of Spain?

I'm not sure.

Title II, which describes how bills are passed was created in what year?

I'm not sure.

The sovereign has 25 days to give his or her assent according to what article?

I'm not sure.

The monarch does not have a right to call for a referendum according to which article?

I'm not sure.


No provision within the constitution grants the monarch an ability to veto legislation directly; however, no provision prohibits the sovereign from withholding royal assent, which effectively constitutes a veto. When the Spanish media asked King Juan Carlos if he would endorse the bill legalising same-sex marriages, he answered "Soy el Rey de España y no el de Bélgica" ("I am the King of Spain and not that of Belgium")—a reference to King Baudouin I of Belgium, who had refused to sign the Belgian law legalising abortion. The King gave royal assent to Law 13/2005 on 1 July 2005; the law was gazetted in the Boletín Oficial del Estado on 2 July and came into effect on 3 July 2005. Likewise, in 2010, King Juan Carlos gave royal assent to a law permitting abortion on demand.

What was King Juan Carlos' response to the media when asked if he would sign a bill supporting same-sex marriage?

"Soy el Rey de España y no el de Bélgica"

What other controversial bill did the king give his assent to in 2010?

a law permitting abortion on demand

When did same-sex marriages become legal in Spain?

3 July 2005


If the Spanish monarch ever refused in conscience to grant royal assent, a procedure similar to the Belgian handling of King Baudouin's objection would not be possible under the current constitution. If the sovereign were ever declared incapable of discharging royal authority, his or her powers would not be transferred to the Cabinet, pending the parliamentary appointment of a regency. Instead, the constitution mandates the next person of age in the line of succession would immediately become regent. Therefore, had Juan Carlos followed the Belgian example in 2005 or 2010, a declaration of incapacity would have transferred power to Felipe, then the heir apparent.

If the Spanish monarch is deemed incapable of granting assent, who is the power transferred to?

the next person of age in the line of succession

Could a Spanish ruler follow the same action of events as King Baudouin did in Belgium?

not be possible under the current constitution

If the Spanish sovereign was found capable of discharging royal authority, what happens?

I'm not sure.

If Juan Carlos had been declared capable, who would have been given power?

I'm not sure.

Who is the current heir apparent to Juan Carlos?

I'm not sure.

Who gets power if the sovereign were declared capable?

I'm not sure.


Articles 41 and 68 of the constitution empower the sovereign to withhold royal assent from bills adopted by the Legislative Assembly. In 2010, the kingdom moved towards greater democracy, with King George Tupou V saying that he would be guided by his prime minister in the exercising of his powers. Nonetheless, this does not preclude an independent royal decision to exercise a right of veto. In November 2011, the assembly adopted an Arms and Ammunitions (Amendment) Bill, which reduced the possible criminal sentences for the illicit possession of firearms. The bill was adopted by ten votes to eight. Two members of the assembly had recently been charged with the illicit possession of firearms. The Prime Minister, Lord Tuʻivakanō, voted in favour of the amendment. Members of the opposition denounced the bill and asked the King to veto it, which he did in December.

Which articles allow the soverign to refise consent even when the bills have been passed through the Legislative assembly?

41 and 68

What statement by King George Tupou emphasized democracy?

he would be guided by his prime minister in the exercising of his powers

In which year was the Arms and Ammunitions (Amemndment) Bill adopted?

In what month did the King veto the Arms and Ammunitions Amendment Bill?

December

What articles empower the sovereign to grant royal assent?

I'm not sure.

The kingdom moved away from democracy in what year?

I'm not sure.

An Art and Ammunitions Bill was adopted in what year?

I'm not sure.

What bill was adopted by eight votes to ten?

I'm not sure.

How many member of the assembly were charge with legal possession of firearms?

I'm not sure.


In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely. It allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.

What is an arithmetical structure comprising of a set of elements including an operation that joins any two elements to form a third element?

a group

What is the name used to describe the four conditions of closure, associativity, identity and invertibility?

group axioms

What permits elements with different mathematical starting points to be taken care of in a flexible manner while holding their key basic aspects?

abstract formalization of the group axioms

What is a set of elements constructed from?

I'm not sure.

What are the two elements called?

I'm not sure.

What is the abstract formalization attached to?

I'm not sure.

What do entities lose when handled in abstract algebra?

I'm not sure.

What is an example of a rare group?

I'm not sure.


Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincaré groups can express the physical symmetry underlying special relativity.

What shares an essential relationship to groups?

symmetry

What are the symmetry groups utilized as a part of the Standard Model particle physics?

Lie groups

What groups are are utilized toward comprehending symmetry wonders in chemistry?

Point groups

What groups can express the physical symmetry hidden behind special relativity?

Poincaré groups

What encodes a symmetry group?

I'm not sure.

What are groups dissimilar to?

I'm not sure.

Point groups are used in what form of physics?

I'm not sure.

Poincare groups are used to understand molecular what?

I'm not sure.

What do Lie groups express in terms of special relativity?

I'm not sure.


The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right.a[›] To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely (its group representations), both from a theoretical and a computational point of view. A theory has been developed for finite groups, which culminated with the classification of finite simple groups announced in 1983.aa[›] Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.

Where did the idea of a group come from?

the study of polynomial equations,

When was the group notion summed up and solidly settled?

What are smaller and easier to understand groups broken down into?

subgroups, quotient groups and simple groups.

When was announcement for the classification of finite simple groups?

Who generalized group notion in 1870?

I'm not sure.

What year did mathematicians begin studying groups in their own right?

I'm not sure.

What are the two subgroups?

I'm not sure.

When did theorists begin exploring the theoretical and computational point of view?

I'm not sure.

When did the geometric group theory become less active?

I'm not sure.


The set G is called the underlying set of the group (G, •). Often the group's underlying set G is used as a short name for the group (G, •). Along the same lines, shorthand expressions such as "a subset of the group G" or "an element of group G" are used when what is actually meant is "a subset of the underlying set G of the group (G, •)" or "an element of the underlying set G of the group (G, •)". Usually, it is clear from the context whether a symbol like G refers to a group or to an underlying set.

What is known as underlying set of the group?

The set

What is often utilized as a short name for the group?

the group's underlying set

What expressions are utilized when is really implied to be a longer expression?

shorthand expressions

What cannot be used as the short name for the group?

I'm not sure.

What is the overlaying set of the group?

I'm not sure.

What can be unclear for the G symbol?

I'm not sure.

A subset of the underlying set G of the group (G) cannot be written using what kind of expression?

I'm not sure.


These symmetries are represented by functions. Each of these functions sends a point in the square to the corresponding point under the symmetry. For example, r1 sends a point to its rotation 90° clockwise around the square's center, and fh sends a point to its reflection across the square's vertical middle line. Composing two of these symmetry functions gives another symmetry function. These symmetries determine a group called the dihedral group of degree 4 and denoted D4. The underlying set of the group is the above set of symmetry functions, and the group operation is function composition. Two symmetries are combined by composing them as functions, that is, applying the first one to the square, and the second one to the result of the first application. The result of performing first a and then b is written symbolically from right to left as

What sends a point in the square to the relating point under the symmetry?

functions

What gives another symmetry function?

Composing two of these symmetry functions

What group includes the symmetries of degree 4 and denoted D4?

the dihedral group

What are represented by symmetries?

I'm not sure.

r1 is part of what group?

I'm not sure.

Both symmetries are applied to what?

I'm not sure.

What is written from left to right?

I'm not sure.

How many degrees is fh rotated?

I'm not sure.


The modern concept of an abstract group developed out of several fields of mathematics. The original motivation for group theory was the quest for solutions of polynomial equations of degree higher than 4. The 19th-century French mathematician Évariste Galois, extending prior work of Paolo Ruffini and Joseph-Louis Lagrange, gave a criterion for the solvability of a particular polynomial equation in terms of the symmetry group of its roots (solutions). The elements of such a Galois group correspond to certain permutations of the roots. At first, Galois' ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups were investigated in particular by Augustin Louis Cauchy. Arthur Cayley's On the theory of groups, as depending on the symbolic equation θn = 1 (1854) gives the first abstract definition of a finite group.

What modern concept was created from many fields of mathematics?

abstract group

The journey for answers to polynomial equations of degree higher than 4 was the original motivation for what theory?

group theory

Which French mathematician expanded on earlier work of Paolo Ruffini and Joseph-Louis Lagrange?

Évariste Galois

Who developed a theory giving the first abstract definition of a finite group?

Arthur Cayley

People were looking for polynomial equations under what number?

I'm not sure.

Whose work did Paolo Ruffini and Joseph-Louis Lagrange base their work on?

I'm not sure.

What was Augustin Louis Cauchy's nationality?

I'm not sure.

When did Arthur Cayley publish On the theory of groups?

I'm not sure.

What equation did Galois create that created an abstract definition?

I'm not sure.


The convergence of these various sources into a uniform theory of groups started with Camille Jordan's Traité des substitutions et des équations algébriques (1870). Walther von Dyck (1882) introduced the idea of specifying a group by means of generators and relations, and was also the first to give an axiomatic definition of an "abstract group", in the terminology of the time. As of the 20th century, groups gained wide recognition by the pioneering work of Ferdinand Georg Frobenius and William Burnside, who worked on representation theory of finite groups, Richard Brauer's modular representation theory and Issai Schur's papers. The theory of Lie groups, and more generally locally compact groups was studied by Hermann Weyl, Élie Cartan and many others. Its algebraic counterpart, the theory of algebraic groups, was first shaped by Claude Chevalley (from the late 1930s) and later by the work of Armand Borel and Jacques Tits.

When did the uniform theory of groups develop from different sources?

Who presented a method for specifying a group by means of generators and relations?

Walther von Dyck

What theory did Hermann Weyl study in addition to locally compact groups?

The theory of Lie groups

Who initially molded the theory of algebraic groups?

Claude Chevalley

What did Walter von Dyck publish in 1870?

I'm not sure.

Who wrote the theory of Lie groups?

I'm not sure.

What did Jacques Tits shape first?

I'm not sure.

What was Issai Schur's theory on?

I'm not sure.

Who worked on representation theory of lie groups?

I'm not sure.


The University of Chicago's 1960–61 Group Theory Year brought together group theorists such as Daniel Gorenstein, John G. Thompson and Walter Feit, laying the foundation of a collaboration that, with input from numerous other mathematicians, classified all finite simple groups in 1982. This project exceeded previous mathematical endeavours by its sheer size, in both length of proof and number of researchers. Research is ongoing to simplify the proof of this classification. These days, group theory is still a highly active mathematical branch, impacting many other fields.a[›]

Where did the group of theorists first meet?

The University of Chicago

What university class year belonged to the group of theorists?

What did the group of theorists classify in 1982?

all finite simple groups

What two factors describe the large size of the project?

length of proof and number of researchers.

What was classified in 1960?

I'm not sure.

Who founded the University of Chicago's Group Theory Year?

I'm not sure.

What no longer has much impact on other fields?

I'm not sure.

What was shorter about this project as compared to other endeavors?

I'm not sure.

When did the University of Chicago begin?

I'm not sure.


To understand groups beyond the level of mere symbolic manipulations as above, more structural concepts have to be employed.c[›] There is a conceptual principle underlying all of the following notions: to take advantage of the structure offered by groups (which sets, being "structureless", do not have), constructions related to groups have to be compatible with the group operation. This compatibility manifests itself in the following notions in various ways. For example, groups can be related to each other via functions called group homomorphisms. By the mentioned principle, they are required to respect the group structures in a precise sense. The structure of groups can also be understood by breaking them into pieces called subgroups and quotient groups. The principle of "preserving structures"—a recurring topic in mathematics throughout—is an instance of working in a category, in this case the category of groups.

What ideas are used to understand groups beyond symbols?

structural concepts

What has to be compatible with the group operation?

constructions related to groups

What concept describes groups that can be related to each other via functions?

group homomorphisms

What is needed to understand structural concepts?

I'm not sure.

Both groups and sets have what?

I'm not sure.

What function is used to break groups into pieces?

I'm not sure.

Groups do not need to respect structures in what sense?

I'm not sure.

What is an example of a subgroup?

I'm not sure.


Two groups G and H are called isomorphic if there exist group homomorphisms a: G → H and b: H → G, such that applying the two functions one after another in each of the two possible orders gives the identity functions of G and H. That is, a(b(h)) = h and b(a(g)) = g for any g in G and h in H. From an abstract point of view, isomorphic groups carry the same information. For example, proving that g • g = 1G for some element g of G is equivalent to proving that a(g) ∗ a(g) = 1H, because applying a to the first equality yields the second, and applying b to the second gives back the first.

What are two groups called if they include homomorphisms?

isomorphic

What similar element do isomorphic groups carry?

isomorphic groups

How can showing the second equality yields the first prove the concept of isomorphic groups?

applying a to the first equality yields the second

What are two groups called if no group homomorphisms are found?

I'm not sure.

Isomorphic groups carry different what?

I'm not sure.

What gives the identity of a?

I'm not sure.

From what point of view do isomorphic groups have different information?

I'm not sure.

How does the second equality disprove the concept of isomorphic groups?

I'm not sure.


In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270° for 90°, 180° for 180°, and 90° for 270° (note that rotation in the opposite direction is not defined). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g−1h ∈ H for all elements g, h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[›]

What is composed of two rotations?

a rotation

What rotation can a rotation be reversed by?

inverse

What essential condition must be met for a subset of a group to be a subgroup?

The subgroup test

What is defined when moving in the opposite direction?

I'm not sure.

270 for 180 is an example of what kind of rotation?

I'm not sure.

subgroup R is made up of the inverse and what?

I'm not sure.

What is unimportant for understanding the group as a whole?

I'm not sure.

Knowing the group as a whole is important for understanding what?

I'm not sure.


In many situations it is desirable to consider two group elements the same if they differ by an element of a given subgroup. For example, in D4 above, once a reflection is performed, the square never gets back to the r2 configuration by just applying the rotation operations (and no further reflections), i.e. the rotation operations are irrelevant to the question whether a reflection has been performed. Cosets are used to formalize this insight: a subgroup H defines left and right cosets, which can be thought of as translations of H by arbitrary group elements g. In symbolic terms, the left and right cosets of H containing g are

When is it preferable to consider two group elements to be the same?

irrelevant to the question whether a reflection has been performed

What should not be considered when asking if a reflection has been performed?

rotation operations

What number sets are used to show how subgroups can be seen as translations of the larger group?

Cosets

When are two group elements considered different?

I'm not sure.

In D4 the square can return to the r2 configuration by applying only what?

I'm not sure.

What question are cosets irrelevant to?

I'm not sure.

What does group element g define?

I'm not sure.

When are rotation operations considered?

I'm not sure.


This set inherits a group operation (sometimes called coset multiplication, or coset addition) from the original group G: (gN) • (hN) = (gh)N for all g and h in G. This definition is motivated by the idea (itself an instance of general structural considerations outlined above) that the map G → G / N that associates to any element g its coset gN be a group homomorphism, or by general abstract considerations called universal properties. The coset eN = N serves as the identity in this group, and the inverse of gN in the quotient group is (gN)−1 = (g−1)N.e[›]

What is another term for coset multiplication?

coset addition

What group operation is taken by the set from the original group?

coset multiplication

What group does the inverse of gN include?

quotient group

What is the original group sometimes called?

I'm not sure.

What are group homomorphisms called?

I'm not sure.

What does the Coset gN serve as?

I'm not sure.

What group operation is taken by the original group from the set?

I'm not sure.

The inverse of gN excludes what group?

I'm not sure.


Quotient groups and subgroups together form a way of describing every group by its presentation: any group is the quotient of the free group over the generators of the group, quotiented by the subgroup of relations. The dihedral group D4, for example, can be generated by two elements r and f (for example, r = r1, the right rotation and f = fv the vertical (or any other) reflection), which means that every symmetry of the square is a finite composition of these two symmetries or their inverses. Together with the relations

What groups can be combined to describe every group?

is the quotient of the free group over the generators of the group

What group can be the quotient of the free group over the generators of the group?

any group

What is a finite composition of two symmetries or their inverses?

every symmetry of the square

What do quotient groups describe by themselves?

I'm not sure.

What presentation describes every group?

I'm not sure.

How many elements does the dihedral group generate?

I'm not sure.

What of a square is an infinite composition?

I'm not sure.

Which two elements does D4 generate?

I'm not sure.


Sub- and quotient groups are related in the following way: a subset H of G can be seen as an injective map H → G, i.e. any element of the target has at most one element that maps to it. The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map G → G / N.y[›] Interpreting subgroup and quotients in light of these homomorphisms emphasizes the structural concept inherent to these definitions alluded to in the introduction. In general, homomorphisms are neither injective nor surjective. Kernel and image of group homomorphisms and the first isomorphism theorem address this phenomenon.

What map shows the relation between sub and quotient groups?

injective map

What are the opposites of injective maps?

surjective maps

What is an example of a surjective map?

canonical map

What theory address the phenomenon of homomorphisms being neither injective nor surjective?

the first isomorphism theorem

Subset G of H is seen as what map?

I'm not sure.

What is the minimum number of elements in a target?

I'm not sure.

What kind of map is similar to an injective map?

I'm not sure.

What theory discusses the surjective nature of canonical maps?

I'm not sure.

What two forms must homomorphisms take?

I'm not sure.


Groups are also applied in many other mathematical areas. Mathematical objects are often examined by associating groups to them and studying the properties of the corresponding groups. For example, Henri Poincaré founded what is now called algebraic topology by introducing the fundamental group. By means of this connection, topological properties such as proximity and continuity translate into properties of groups.i[›] For example, elements of the fundamental group are represented by loops. The second image at the right shows some loops in a plane minus a point. The blue loop is considered null-homotopic (and thus irrelevant), because it can be continuously shrunk to a point. The presence of the hole prevents the orange loop from being shrunk to a point. The fundamental group of the plane with a point deleted turns out to be infinite cyclic, generated by the orange loop (or any other loop winding once around the hole). This way, the fundamental group detects the hole.

What are usually analyzed by associating groups to them and studying the elements of the corresponding groups?

Mathematical objects

Who founded algebraic topology?

Henri Poincaré

What did Henri Poincaré introduce when he established algebraic topology?

the fundamental group

What topological properties translate into properties of groups?

proximity and continuity

What represents elements of the fundamental group?

loops

Who first applied groups to other mathematical areas?

I'm not sure.

Which topological properties do not carry over into groups?

I'm not sure.

Why is the blue loop considered relevant?

I'm not sure.

What causes the orange loop to shrink to a point?

I'm not sure.

What results in a finite cycle?

I'm not sure.


In modular arithmetic, two integers are added and then the sum is divided by a positive integer called the modulus. The result of modular addition is the remainder of that division. For any modulus, n, the set of integers from 0 to n − 1 forms a group under modular addition: the inverse of any element a is n − a, and 0 is the identity element. This is familiar from the addition of hours on the face of a clock: if the hour hand is on 9 and is advanced 4 hours, it ends up on 1, as shown at the right. This is expressed by saying that 9 + 4 equals 1 "modulo 12" or, in symbols,

What positive integer is used to divide the sum of two positive integers in modular mathematics?

the modulus

What results from modular addition?

the remainder of that division

What type of device can be use to demonstrate modular addition?

a clock

How many integers are divided in modular arithmetic?

I'm not sure.

What are the two integers called?

I'm not sure.

What is the result of the remained of the division?

I'm not sure.

What is 9 in modular addition?

I'm not sure.

If the hour hand is on 1 and is advanced by 4 hours, where does it end up?

I'm not sure.


For any prime number p, there is also the multiplicative group of integers modulo p. Its elements are the integers 1 to p − 1. The group operation is multiplication modulo p. That is, the usual product is divided by p and the remainder of this division is the result of modular multiplication. For example, if p = 5, there are four group elements 1, 2, 3, 4. In this group, 4 · 4 = 1, because the usual product 16 is equivalent to 1, which divided by 5 yields a remainder of 1. for 5 divides 16 − 1 = 15, denoted

What term describes the group of integers related to a prime number?

modulo p

What integers are included in modulo p?

1 to p − 1

How many group elements exist if p=5?

four group elements

What describes a group of integers related to a modulo?

I'm not sure.

What is the result of modular multiplication divided by?

I'm not sure.

How many integers does p = 5 have?

I'm not sure.

What is p divided by?

I'm not sure.

What is 16 multiplied by 5 If p=5?

I'm not sure.


In the groups Z/nZ introduced above, the element 1 is primitive, so these groups are cyclic. Indeed, each element is expressible as a sum all of whose terms are 1. Any cyclic group with n elements is isomorphic to this group. A second example for cyclic groups is the group of n-th complex roots of unity, given by complex numbers z satisfying zn = 1. These numbers can be visualized as the vertices on a regular n-gon, as shown in blue at the right for n = 6. The group operation is multiplication of complex numbers. In the picture, multiplying with z corresponds to a counter-clockwise rotation by 60°. Using some field theory, the group Fp× can be shown to be cyclic: for example, if p = 5, 3 is a generator since 31 = 3, 32 = 9 ≡ 4, 33 ≡ 2, and 34 ≡ 1.

What is a group labeled when the element 1 is primitive?

cyclic

What group is isomorphic to cyclic groups?

Any cyclic group with n elements

What example of cyclic group satisfies the express of zn = 1?

the group of n-th complex roots of unity

A cyclic group without n elements is considered what?

I'm not sure.

What element is not primitive in groups Z/nZ?

I'm not sure.

What are groups called when element 1 is not primitive?

I'm not sure.

What rotation results in multiplying but n?

I'm not sure.

What are numbers on an irregular n-gon?

I'm not sure.


Symmetry groups are groups consisting of symmetries of given mathematical objects—be they of geometric nature, such as the introductory symmetry group of the square, or of algebraic nature, such as polynomial equations and their solutions. Conceptually, group theory can be thought of as the study of symmetry.t[›] Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object X if every group element performs some operation on X compatibly to the group law. In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too). By a group action, the group pattern is connected to the structure of the object being acted on.

What are groups consisting of symmetries of given arithmetic concepts?

Symmetry groups

What term describes the introductory symmetry group of the square?

geometric nature

What can regarded as the study of symmetry?

group theory

What is the name of the rule that must be met for a group operation to occur?

group law

The group pattern is connected to the structure of the target by what behavior?

group action

What do symmetry groups make?

I'm not sure.

Which equation is are used for the square?

I'm not sure.

What is the study of geometrical or analytical objects called?

I'm not sure.

What makes the study of symmetries easier?

I'm not sure.

What does group action do to the tiling?

I'm not sure.


Likewise, group theory helps predict the changes in physical properties that occur when a material undergoes a phase transition, for example, from a cubic to a tetrahedral crystalline form. An example is ferroelectric materials, where the change from a paraelectric to a ferroelectric state occurs at the Curie temperature and is related to a change from the high-symmetry paraelectric state to the lower symmetry ferroelectic state, accompanied by a so-called soft phonon mode, a vibrational lattice mode that goes to zero frequency at the transition.

What aids in predicting changes of physical traits?

group theory

What stage of a physical transformation can group theory be used to make prediction?

phase transition

What temperature causes the change of ferroelectric materials?

Curie temperature

What term describes the vibrational lattice mode that turns to 0 frequency at the change?

soft phonon mode

What predicts the changes in group theory?

I'm not sure.

Which stage can physical properties be used to make predictions about group theory?

I'm not sure.

What temperature causes a change from ferroelectric to paraelectric?

I'm not sure.

What is the frequency of a paraelectric state before transition?

I'm not sure.

What is the name of the mode that moves material from a low-symmetry state to a high one?

I'm not sure.


Finite symmetry groups such as the Mathieu groups are used in coding theory, which is in turn applied in error correction of transmitted data, and in CD players. Another application is differential Galois theory, which characterizes functions having antiderivatives of a prescribed form, giving group-theoretic criteria for when solutions of certain differential equations are well-behaved.u[›] Geometric properties that remain stable under group actions are investigated in (geometric) invariant theory.

What are examples of finite symmetry groups used in coding theory?

Mathieu groups

What is used for error correction of transferred data?

coding theory

What describes functions having antiderivatives of a prescribed form?

differential Galois theory

What concept investigates geometric elements that stay stable under group action?

invariant theory

What theory is error correction applied to?

I'm not sure.

Which form of finite symmetry groups are useless in coding theory?

I'm not sure.

Mathieu groups have what kind of prescribed form?

I'm not sure.

What stable properties does the Galois theory study?

I'm not sure.

Geometric Invariant theory studies what kind of equations?

I'm not sure.


Matrix groups consist of matrices together with matrix multiplication. The general linear group GL(n, R) consists of all invertible n-by-n matrices with real entries. Its subgroups are referred to as matrix groups or linear groups. The dihedral group example mentioned above can be viewed as a (very small) matrix group. Another important matrix group is the special orthogonal group SO(n). It describes all possible rotations in n dimensions. Via Euler angles, rotation matrices are used in computer graphics.

What groups combine matrices with matrix multiplication?

Matrix groups

What includes all invertible n-by-n matrices with real entries?

The general linear group

What term describes subgroups of the general linear group?

matrix groups

What matrix group portrays all possible rotations in n dimensions?

the special orthogonal group SO(n)

Rotation matrix groups are utilized in computer graphics with what concept?

Euler angles

What are matrices and matrix groups combined called?

I'm not sure.

The general linear group describes all possible what?

I'm not sure.

What is an example of a large matrix group?

I'm not sure.

What are subgroups of the special orthogonal group called?

I'm not sure.

What type of angles are made of all invertible n-by-b matrices?

I'm not sure.


Exchanging "+" and "−" in the expression, i.e. permuting the two solutions of the equation can be viewed as a (very simple) group operation. Similar formulae are known for cubic and quartic equations, but do not exist in general for degree 5 and higher. Abstract properties of Galois groups associated with polynomials (in particular their solvability) give a criterion for polynomials that have all their solutions expressible by radicals, i.e. solutions expressible using solely addition, multiplication, and roots similar to the formula above.

What degree does not include simple formulas for cubic and quatric equations?

degree 5 and higher

What concept is associated with the solvability of polynomials?

Abstract properties of Galois groups

What are used to express the solutions of polynomials?

radicals

What degree must it be lower than to have simple formulas?

I'm not sure.

What give criterion for abstract properties?

I'm not sure.

Which group cannot be expressed using radicals?

I'm not sure.

What is an example of a complex operation?

I'm not sure.

What do cubic and quartic equations not have?

I'm not sure.


A group is called finite if it has a finite number of elements. The number of elements is called the order of the group. An important class is the symmetric groups SN, the groups of permutations of N letters. For example, the symmetric group on 3 letters S3 is the group consisting of all possible orderings of the three letters ABC, i.e. contains the elements ABC, ACB, ..., up to CBA, in total 6 (or 3 factorial) elements. This class is fundamental insofar as any finite group can be expressed as a subgroup of a symmetric group SN for a suitable integer N (Cayley's theorem). Parallel to the group of symmetries of the square above, S3 can also be interpreted as the group of symmetries of an equilateral triangle.

What does a finite group include?

a finite number of elements

What is the number of elements in a group named?

the order of the group

What type of class has a finite group that can be expressed as a subgroup of a symmetric group?

fundamental

What can be described as the group of symmetries of an equilateral triangle?

What is called the order of the group?

I'm not sure.

What does a finite number of elements include?

I'm not sure.

What can a subgroup of a symmetric group SN can be expressed as?

I'm not sure.

What are the group of symmetries of a S3?

I'm not sure.


Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.

What level of finality do mathematicians try to reach with math concepts?

complete classification

What area of classification leads to troublesome arithmetic?

finite groups

What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?

Lagrange's theorem

What can be used to classify small groups even though there is no classification of all finite groups?

Computer algebra systems

What describes finite simple groups as the building pieces for all finite groups?

The Jordan–Hölder theorem

Both p2 and p3 are what?

I'm not sure.

What is used to classify all finite groups?

I'm not sure.

When was the Jordan-Holder theorem published?

I'm not sure.

What did Richard Borcherd make a complete classification of?

I'm not sure.

What theorem details the link between the largest finite group and modular functions?

I'm not sure.