* In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation.

Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.

; Metropolitan bishop: A metropolitan bishop is an archbishop in charge of an ecclesiastical province, or group of dioceses, and in addition to having immediate jurisdiction over his own archdiocese, also exercises some oversight over the other dioceses within that province.

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

In addition, other assaults, robbery, tiger kidnapping, extortion, fuel laundering and smuggling were undertaken by the group.

In addition to igniting spontaneously in air, it reacts explosively with water even at low temperatures, more so than other members of the first group of the periodic table.

If the addition of a functional group takes place at the less substituted carbon atom of the double bond, then the electrophilic substitution with acids is not possible.

While the addition to the electron-rich alkenes and alkynes is mainly electrophilic, the nucleophilic addition plays an important role for the carbon-heteroatom multiple bonds, and especially its most important representative, the carbonyl group.

During his recovery from a heart attack late in 1955, he huddled with his closest advisors to evaluate the GOP's potential candidates ; the group, in addition to his doctor, concluded a second term was well advised, and he announced in February 1956 he would run again.

These age groups roughly correspond to those standardized by FINA, with the addition of a youngest age group for divers 9 and younger, Group E, which does not compete nationally and does not have a tower event ( although divers of this age may choose to compete in Group D ).

This led to the addition of the number sign (#, sometimes called ' octothorpe ,' ' pound ' or ' diamond ' in this context-' hash ' or ' gate ' in the UK ) and asterisk or " star " (*) keys as well as a group of keys for menu selection: A, B, C and D. In the end, the lettered keys were dropped from most phones, and it was many years before these keys became widely used for vertical service codes such as * 67 in the United States of America and Canada to suppress caller ID.

* If we think of as the group of real numbers under addition, then the direct product still consists of.

Additive notation is typically used when numerical addition or a commutative operation other than multiplication interprets the group operation ;

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with " compatible " being formalized by distributivity, and the caveat that the additive identity ( 0 ) has no multiplicative inverse ( one cannot divide by 0 ).

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

Her personal letters to leaders of the Revolution influenced policy ; in addition, she often hosted political gatherings of the Brissotins, a political group which allowed women to join.

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.

In addition, Hayek attracted an exceptionally able group of students who were dedicated to a libertarian ideology.

In addition to his cosmological writings, Bruno also wrote extensively on the art of memory, a loosely organized group of mnemonic techniques and principles.

In addition to the original Broadway and London cast recordings, and the motion picture soundtrack ( no longer available ), there are recordings of the 1990 studio cast, the 1995 Royal National Theatre revival ( starring Judi Dench ), and the 2001 Barcelona cast recording sung in Catalan.

Session rosters from 1938 show both " lead guitar " and " electric guitar " in addition to guitar and steel guitar in the Texas Playboys recordings.

In addition to failures regarding comprehensive recordings, as one additional example, Robert Gellately and Simon Sebag-Montefiore argue that the many suspects beaten and tortured to death while in " investigative custody " were likely not to have been counted amongst the executed.

Meeker's recording was selected by the Library of Congress as a 2010 addition to the National Recording Registry, which selects recordings annually that are " culturally, historically, or aesthetically significant ".

In addition to electronic resources, printed books and journals, the Library also acquires works in microform, sound recordings, videos and other media consistent with the University's academic programme needs.

In addition, Bill Haley and the Comets also scored chart hits in Latin America, Mexico, and India during the period 1961 – 1966 with recordings such as " Twist Español ", " Florida Twist ", " Spanish Twist ", " Caravan Twist ", and " Land of a Thousand Dances ".

In addition to featuring the majority of Prince's hit singles ( with the exception of " Batdance " and other songs that appeared on the Batman soundtrack ), The Hits includes an array of previously hard-to-find recordings, notably B-sides spanning the majority of Prince's career, as well as a handful of previously unreleased tracks such as the Revolution-recorded " Power Fantastic " and a live recording of " Nothing Compares 2 U " with Rosie Gaines.

In addition the new hit artist Ritchie Valens ,, J. P. " The Big Bopper " Richardson and Dion DiMucci, joined the tour to promote their recordings and to make an extra profit.

In addition, recordings of the 1952 episodes " Man of Mystery ", " Murder on the Riviera " and " Blackmail is a Nasty Word " are included on the Criterion Collection DVD The Complete Mr. Arkadin.

Off-air home audio recordings of various television programmes have also been recovered, at least preserving the soundtracks to otherwise missing shows, and some of these ( particularly from Doctor Who ) have been released on CD by the BBC following restoration and the addition of narration to describe purely visual elements.

While the band reformed in the early 90s with the addition of former Strawmen members David Leonhardt ( guitar ) and Harmon, the live album 88 and Sticks and Stones, a collection of previously unreleased recordings and demos, were released.

In addition to musical performances, Phillips recorded events such as weddings and funerals, selling the recordings.

In addition to his own recordings, Norman produced music on his Solid Rock label for Randy Stonehill, Mark Heard, Tom Howard, Pantano / Salsbury, David Edwards, and Salvation Air Force.

In addition to producing, Parks has released six studio albums of his own recordings: Song Cycle, Discover America, Clang of the Yankee Reaper, Jump !, Tokyo Rose, and with Brian Wilson, Orange Crate Art.

In addition, a number of headphone amplifier companies have created hardware that takes advantage of these special recordings.

Choral Evensong ( or, on red-letter days, Holy Mass ) is currently sung on Tuesdays, Fridays and Sundays during full term, in addition to which the Choir sings for Gaudy Evensongs, for Special Feasts and Ceremonies ( including the All Souls Requiem, Remembrance, the Advent and Christmas Carol Services, Ash Wednesday, and the Passiontide service ) and for frequent concerts, commercial events, foreign tours, CD recordings and broadcasts.

A sampling of his versatility in addition to numerous recordings of the standard classical repertoire would include his recordings of Baroque pieces using period instruments ; American bluegrass music ; traditional Chinese melodies including the soundtrack to the film Crouching Tiger Hidden Dragon ; the tangos of Argentinian composer Ástor Piazzolla ; an eclectic and unusual collaboration with Bobby McFerrin ( where Ma admitted to being terrified of the improvisation McFerrin pushed him toward ); as well as the music of modern minimalist Philip Glass in such works as the 2002 piece Naqoyqatsi.

Tomlin was an instant success on the already established program, in which in addition to appearing in general sketches and delivering comic gags, she began appearing as regular characters she created that quickly became famous and went on to lives outside of the show in later recordings and television specials:

In addition to commercial recordings, the BBC Legends label has issued six CDs of radio performances from the 1960s with Silvestri conducting the Bournemouth Orchestra.

In addition to a vast catalog of recordings created with the ensemble's music directors, the orchestra has made many recordings with guest conductors Vladimir Ashkenazy, Oliver Knussen, Kurt Sanderling, Yoel Levi, Riccardo Chailly, Michael Tilson Thomas, and Louis Lane ( the orchestra's longtime Associate Conductor ).

In addition to weekly broadcasts on the NBC Red and Blue networks, the NBC Symphony Orchestra made many recordings for RCA Victor of symphonies, choral music and operas.

In addition, there are many recordings available of his broadcast performances, as well as his remarkable rehearsals with the NBC Symphony.