In mathematics, specifically group theory, a quotient group ( or factor group ) is a group obtained by identifying together elements of a larger group using an equivalence relation.

For example, the cyclic group of addition modulo n can be obtained from the integers by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class ( known as a congruence class ) as a single entity.

On the first day of the tournament, a bout of individual jousting, a mysterious masked knight, identifying himself only as " Desdichado " ( which is described in the book as Spanish for the " Disinherited One ", though actually meaning " Unfortunate "), makes his appearance and manages to defeat some of the best Norman lances, including Bois-Guilbert, Maurice de Bracy, a leader of a group of " Free Companions " ( mercenary knights ), and the baron Reginald Front-de-Boeuf.

This theory provides an attempt of identifying general relativity and the standard model within the Lie group E8.

Various studies in this regard so far yield differing results for identifying the exact sister group: in one case the Placozoa would qualify as the nearest relatives of the Cnidaria, while in another they would be a sister group to the Ctenophora, and occasionally they are placed directly next to the Bilateria:

For identifying the channel to which a packet is associated, each packet contains a 12 bit logical channel identifier made up of an 8-bit logical channel number and a 4-bit logical channel group number.

Language is a primary and dominant identifying factor of a people group.

On the Let it Be album where Preston's performances are used the song credits list " with Billy Preston ", clearly identifying him as separate from the main group, yet also giving him a level of individuality that separated him from studio session players.

A gang is a group of recurrently associating individuals with identifiable leadership and internal organization, identifying with or claiming control over territory in a community, and engaging either individually or collectively in violent or other forms of illegal behavior.

In the 1990s a group of concerned landowners, individuals and real estate developers formed the Northern Edwards Aquifer Resource Council ( NEARC ) with the goal of obtaining a United States Fish and Wildlife Service 10-A permit ( known as an Incidental Take Permit ) for the entire county by identifying and preserving a sufficient number of caves with endangered species to ensure survival of the species.

Multiple alignments are often used in identifying conserved sequence regions across a group of sequences hypothesized to be evolutionarily related.

Examples includes mechanisms for dealing with status, reciprocity, identifying cheaters, ostracism, altruism, group decision, leadership, and intergroup relations.

Additionally, from the social identity approach, group formation involves both identifying with some individuals and explicitly not identifying with others.

Of the roughly 64 % identifying as Christian, the largest proportions were either Roman Catholic ( 25. 8 %) or Anglican ( 18. 7 %), with the third largest group being the 5. 7 % affiliated with the Uniting Church.

Botanists Ken Hill and Lawrie Johnson were the first to define the genus Corymbia in 1995, identifying the bloodwoods, ghost gums and spotted gums as a group distinct from Eucalyptus.

In the latter part of the 1960s, a group of black Bahians began dressing as Native Americans during the Salvadoran Carnaval, identifying with their shared struggles through history.

Starting in 1974, a group of black Bahians called Ilê Aiyê became prominent, identifying with the Yoruba people and Igbo people of West Africa.

The group, upon the issuance of its first press release on December 21, 1957, designated itself a `` Committee of Investigation ''.

The development of abstract algebra brought with itself group theory, rings and fields, Galois theory.

* A group automorphism is a group isomorphism from a group to itself.

** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).

In the case of groups, the inner automorphisms are the conjugations by the elements of the group itself.

The experimental protocol used in Carlson's study was agreed to by a group of physicists and astrologers prior to the actual experiment itself.

The group calls itself " Al-Harakat Al-Islamiyya " or the " Islamic Movement ".

The ELN guerrilla had been seriously crippled by military operations in the region of Anorí by 1974, but it managed to reconstitute itself and escape destruction, in part due to the administration of Alfonso López Michelsen ( 1974 – 1978 ) allowing it to escape encirclement, hoping to initiate a peace process with the group.

On the 1963 Aldermaston march, a clandestine group calling itself Spies for Peace distributed leaflets about a secret government establishment, RSG 6, that the march was passing.

On August 19, 1991, a day before the New Union Treaty was to be signed devolving power to the republics, a group calling itself the " State Emergency Committee " seized power in Moscow declaring that Gorbachev was ill and therefore relieved of his position as president.

The Misurasata movement split in 1983, with the breakaway Misura group of Stedman Fagoth Muller allying itself more closely with the FDN, and the rest accommodating themselves with the Sandinista government.

Other ecclesias throughout the world which supported them became known as the " Suffolk Street fellowship " to distinguish itself from the group they were separated from, which became known as the " Temperance Hall fellowship ".

By now the group had become a de-facto political force, pitting itself against rising elements of American social and political life such as the religious right, Ronald Reagan and the idle rich.

A group speaking a separate " language " is often seen as having a greater claim to being a separate " people ", and thus to be more deserving of its own independent state, while a group speaking a " dialect " tends to be seen not as " a people " in its own right, but as a sub-group, part of a bigger people, which must content itself with regional autonomy.

Although Dada itself was unknown in Georgia until at least 1920, from 1917-1921 a group of poets called themselves " 41st Degree " ( referring both to the latitude of Tbilisi, Georgia and to the temperature of a high fever ) organized along Dadaist lines.

Thus the probability of two failures in a same RAID group in time proximity is much smaller ( approximately the probability squared, i. e., multiplied by itself ).

If a database cannot tolerate even such smaller probability of data loss, then the RAID group itself is replicated ( mirrored ).

Thus the probability of two failures in a same RAID group in time proximity is much smaller ( approximately the probability squared, i. e., multiplied by itself ).

If a database cannot tolerate even such smaller probability of data loss, then the RAID group itself is replicated ( mirrored ).

Electronegativity, symbol < span class =" nounderlines "> χ </ span >, is a chemical property that describes the tendency of an atom or a functional group to attract electrons ( or electron density ) towards itself.

After extensive debates, the Assembly sent its final proposal to the Council's Committee of Ministers, which convened a group of experts to draft the Convention itself.

William Hague hoped to put the issue to rest by negotiating a new arrangement in 1999 by which the parliamentary group would rebrand itself as " EPP-ED ", with the " European Democrat " nomenclature returning after a seven-year hiatus.

* Another group is the School of the Military that studied strategy and the philosophy of war ; Sunzi and Sun Bin were influential leaders.

On 15 August 1909 the Military League, a group of Greek officers, took action against the government to reform their country's national government and reorganize the army.

The group that finally overthrew President Patassé consisted of – in addition to Bozizé's own rebels – 100 soldiers from Chad's Military.

In the 2005 – 06 academic year, the Columbia Military Society, Columbia's student group for ROTC cadets and Marine officer candidates, was renamed the Hamilton Society for " students who aspire to serve their nation through the military in the tradition of Alexander Hamilton ".

On 16 April 2012 Military leaders and a group of political parties in Guinea-Bissau have announced the formation of a Transitional National Council.

The 1929 Palestine riots ( see also the Hebron Massacre ), led Ze ' ev Jabotinsky to create a right-wing militia group called the Irgun Tzvai Leumi ( National Military Organization, known in Hebrew by its acronym " Etzel ").

Under a January 1986 Military Council decree, state executive and legislative powers were transferred to the King who was to act on the advice of the Military Council, a self-appointed group of leaders of the Royal Lesotho Defense Force ( RLDF ).

The Daily Mail reports that Edward has had the photograph independently verified by specialists like a Loch Ness Monster sighting devotee and a group of US Military monster experts.

On November 19, 1968, a group of young officers staged a bloodless coup and set up a 14-member Military Committee for National Liberation ( CMLN ), with Lt. Moussa Traoré as president.

In early 1979, he was pushed aside by another group of officers, who renamed the junta the Military Committee for National Salvation ( CMSN ).

Enterprise is recalled and retrofitted as a warship, with more powerful weapons and a group of elite Military Assault Command Operations ( MACOs ).

The group also held its " First Military School " where members were instructed in military tactics and weapons use.

* Dubai Defence Force-Central Military Command with over 20, 000 men in one infantry brigade group.

The fallen hero was chosen from a group previously interred at Romagne Military Cemetery in France, and was re-interred at Arlington National Cemetery.

Muslim officers named a Christian from a small ethnic group ( the Anga ) in central Nigeria, General Yakubu " Jack " Gowon, as the head of the Federal Military Government ( FMG ).

It was estimated that 54 % of these victims were killed by the extremist guerrilla group Shining Path, 30 % by the Peruvian Military and police forces, and the rest were by rural or peasant self-defense militias.

Commissioned in 1875 by the Pickett Division Association, a group of veterans from his division, it was originally intended to be placed at Gettysburg National Military Park at the " High Water Mark " of Pickett's Charge, but was built in Richmond when the U. S. War Department refused permission for the battlefield placement.

This has included starting the activism groups The Underground Action Alliance, Military Free Zone ( a group to protest a clause in the No Child Left Behind Act, which gave military recruiters automatic access to students ' personal details ) and The Bright Lights.

Hayashi also promoted Fumimaro Konoye's doctrines, as a " right-winger " amongst the militarists, who approved of the " fiction " of democracy, and the Emperor's role with an " adviser group ", against " left-winger " radical militarists, led by Kingoro Hashimoto, wanted a Military Shogunate.

The new group included former Prime Ministers Mitsumasa Yonai, Nobuyuki Abe, and Konoe Fumimaro, all of whom supported Japan's aggressive foreign policy and the right-socialist ideals of Kingoro Hashimoto on creation of a Military Shogunate that would manage the Imperial affairs directly.

In February, Commanding General of Military Region 5 Kouprasith Abhay mounted a coup against the group of generals who had attempted a coup the previous year.

Military leaders of these military forces included August Willich and Feliks Trociński and Captain Christian Zinn On May 17 through 18, 1849, a group of workers and democrats from Trier and neighboring townships stormed the arsenal at Prüm to obtain arms for the insurgents of the uprising.

Another group is the School of the Military ( 兵家 ; Bingjia ) that studied warfare and strategy ; Sunzi and Sun Bin were influential leaders.