ATLAS of Finite Groups explained

Isbn:	978-0-19-853199-9
Pub Date:	December 1985
Publisher:	Oxford University Press
Subject:	Group theory
Pages:	294

The ATLAS of Finite Groups, often simply known as the ATLAS, is a group theory book by John Horton Conway, Robert Turner Curtis, Simon Phillips Norton, Richard Alan Parker and Robert Arnott Wilson (with computational assistance from J. G. Thackray), published in December 1985 by Oxford University Press and reprinted with corrections in 2003 .^{[1] [2]} The book codified and systematized mathematicians' knowledge about finite groups, including some discoveries that had only been known within Conway's group at Cambridge University.^[3] Over the years since its publication, it has proved to be a landmark work of mathematical exposition.^[1]

E _{n(2)} ), the character table is not listed and only basic information is given.

The ATLAS is a recognizable large format book (sized 420 mm by 300 mm) with a cherry red cardboard cover and spiral binding.^[7] (One later author described it as "appropriately oversized".^[8] Another noted that his university library shelved it among the oversized geography books.^[9]) The cover lists the authors in alphabetical order by last name (each last name having exactly six letters), which was also the order in which the authors joined the project.^[10] The abbreviations by which the authors refer to certain groups, which occasionally differ from those used by some other mathematicians, are known as "ATLAS notation".^[11]

The book was reappraised in 1995 in the volume The Atlas of Finite Groups: Ten Years on.^[12] It was the subject of an American Mathematical Society symposium at Princeton University in 2015, whose proceedings were published as Finite Simple Groups: Thirty Years of the Atlas and Beyond.^[13]

The ATLAS is being continued in the form of an electronic database, the ATLAS of Finite Group Representations.^[14]

Notes and References

1. Book: Thomas . Breuer . 1603.08650 . Reliability and reproducibility of Atlas information . Gunter . Malle . E. A. . O'Brien . Finite Simple Groups: Thirty Years of the Atlas and Beyond . American Mathematical Society . 21-32 . 2017 . 978-1-470-43678-0 . Contemporary Mathematics . 694.
2. Curtis . Robert T. . John Horton Conway, 26 December 1937 — 11 April 2020 . Biographical Memoirs of Fellows of the Royal Society . 72 . 117–138 . 2022 . 10.1098/rsbm.2021.0034. free .
3. Brian . Denton . none . The Mathematical Gazette . 70 . 453 . 248 . October 1986 . 10.1017/S0025557200139440 .
4. ATLAS, p. vii.
5. 2322937 . The American Mathematical Monthly . 93 . 10 . December 1986 . C85-C91 . Lynn Arthur . none . Steen . etal.
6. R. . Steinberg . none . Mathematics of Computation . 48 . 177 . January 1987 . 441 . 2007904.
7. 10.1090/bull/1744 . R. L. . Griess . Robert Griess . Selected Mathematical Reviews related to the work of John Horton Conway . Bulletin of the American Mathematical Society . etal . 58 . 3 . 443-456 . July 2021 .
8. Peter . Sin . none . 10.4169/000298910x496804 . American Mathematical Monthly . 2010 . 117 . 7 . 657-660.
9. Web site: The Finite Simple Groups. MAA Reviews . Mathematical Association of America . 29 April 2024 . 30 March 2010 . Felipe . Zaldivar .
10. ATLAS, p. xxxii.
11. R. L. . Griess . R. L. Griess . My Life and Times with the Sporadic Simple Groups . Notices of the ICCM . July 2021 . 11-46 . 9 . 1 . 10.4310/ICCM.2021.v9.n1.a2.
12. Book: The atlas of finite groups, ten years on . 1998 . Cambridge, U.K. ; New York, NY, USA : Cambridge University Press . 978-0-521-57587-4 . Internet Archive.
13. Book: Bhargava, Manjul . Finite Simple Groups: Thirty Years of the Atlas and Beyond . Guralnick . Robert . Hiss . Gerhard . Lux . Klaus . Pham . Huu Tiep . 2017 . American Mathematical Society . 2017 . 9781470436780 . Princeton NJ.
14. Web site: ATLAS of Finite Group Representations - V3 .