The ''ATLAS of Finite Groups'', often simply known as the ''ATLAS'', is a
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
book by
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...
,
Robert Turner Curtis,
Simon Phillips Norton,
Richard Alan Parker and
Robert Arnott Wilson
Robert Arnott Wilson (born 1958) is a retired mathematician in London, England, who is best known for his work on classifying the maximal subgroups of finite simple groups and for the work in the Monster group
In the area of abstract alge ...
(with computational assistance from J. G. Thackray), published in December 1985 by
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books ...
and reprinted with corrections in 2003 (). It lists basic information about 93 finite
simple
Simple or SIMPLE may refer to:
*Simplicity, the state or quality of being simple
Arts and entertainment
* ''Simple'' (album), by Andy Yorke, 2008, and its title track
* "Simple" (Florida Georgia Line song), 2018
* "Simple", a song by Johnn ...
groups, the information being generally: its order,
Schur multiplier
In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H_2(G, \Z) of a group ''G''. It was introduced by in his work on projective representations.
Examples and properties
The Schur multiplier \oper ...
,
outer automorphism group In mathematics, the outer automorphism group of a group, , is the quotient, , where is the automorphism group of and ) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually denoted . If is trivial and has a t ...
, various constructions (such as
presentations
A presentation conveys information from a speaker to an audience. Presentations are typically demonstrations, introduction, lecture, or speech meant to inform, persuade, inspire, motivate, build goodwill, or present a new idea/product. Present ...
), conjugacy classes of
maximal subgroup
In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra.
In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' s ...
s (with characters
group action
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...
they define), and, most importantly,
character table In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, and whose columns correspond to conjugacy classes of group elements. The entries consist of characters ...
s (including power maps on the conjugacy classes) of the group itself and bicyclic extensions given by stem extensions and automorphism groups. In certain cases (such as for the
Chevalley groups ), the character table is not listed and only basic information is given.
The ATLAS is a recognizable large format book (sized 420mm by 300mm) with a cherry red cardboard cover and spiral binding. The names of the authors, all six letters long, with initials for the first and second letter, are printed on the cover in the form of an array which evokes the idea of a character table.
The ATLAS is being continued in the form of an electronic database, th
ATLAS of Finite Group Representations
Finite groups
Mathematics books
John Horton Conway
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