Book contents
- Frontmatter
- Contents
- Introduction
- Addresses of registered participants
- Addresses of non-participating authors
- Programme of lectures
- Conference photograph and key
- Symmetric presentations and orthogonal groups
- A constructive recognition algorithm for the special linear group
- Relations in M666
- A survey of symmetric generation of sporadic simple groups
- Harish-Chandra theory, q-Schur algebras, and decomposition matrices for finite classical groups
- The Meataxe as a tool in computational group theory
- Branching rules for modular projective representations of the symmetric groups
- Characters and surfaces: a survey
- On the characterization of finite groups by characters
- Finite linear groups of small degree
- Minimal parabolic systems for the symmetric and alternating groups
- Probabilistic methods in the generation of finite simple groups
- Condensing tensor product modules
- Intersections of Sylow subgroups in finite groups
- Anatomy of the Monster: I
- An integral ‘Meat-axe’
- Finite rational matrix groups: a survey
- Chamber graphs of sporadic group geometries
- An Atlas of sporadic group representations
- Presentations of reductive Fischer groups
- A brief history of the ATLAS
A brief history of the ATLAS
Published online by Cambridge University Press: 19 May 2010
- Frontmatter
- Contents
- Introduction
- Addresses of registered participants
- Addresses of non-participating authors
- Programme of lectures
- Conference photograph and key
- Symmetric presentations and orthogonal groups
- A constructive recognition algorithm for the special linear group
- Relations in M666
- A survey of symmetric generation of sporadic simple groups
- Harish-Chandra theory, q-Schur algebras, and decomposition matrices for finite classical groups
- The Meataxe as a tool in computational group theory
- Branching rules for modular projective representations of the symmetric groups
- Characters and surfaces: a survey
- On the characterization of finite groups by characters
- Finite linear groups of small degree
- Minimal parabolic systems for the symmetric and alternating groups
- Probabilistic methods in the generation of finite simple groups
- Condensing tensor product modules
- Intersections of Sylow subgroups in finite groups
- Anatomy of the Monster: I
- An integral ‘Meat-axe’
- Finite rational matrix groups: a survey
- Chamber graphs of sporadic group geometries
- An Atlas of sporadic group representations
- Presentations of reductive Fischer groups
- A brief history of the ATLAS
Summary
The beginnings of the atlas go back to around 1970 in Cambridge. In about 1969 John Conway had discovered his (then) new simple group 1, and in the ensuing year John Thompson and Conway explored its properties in great detail. One of our aims was to compute the character table of the new group.
This process took more than a year, although most of the time spent was in two short periods at the start and end of that year. In the earlier portion, Mike Guy prepared a computer system for working with character tables—a primitive version of CAS—and in the later one we applied this to a number of starting characters that were produced rather laboriously by hand. Several of the trickiest characters were found by Nick Paterson, and these enabled us to complete the work.
Some time later, we collaborated with Don Livingstone, who used to travel from Birmingham to Cambridge and work overnight with us for the purpose, in finding a number of other character tables.
It then occurred to Conway that some kind of handbook listing “all interesting properties of all interesting groups” would be extremely useful. After taking advice from Frank Adams, he applied to the Science Research Council for a grant to support an assistant to help in producing such a work, and the atlas was born!
The said assistant was Conway's first student in group theory, Robert Curtis, who had just written his thesis on the subgroups of 0, and we gamely set about collecting information about as many groups as we could.
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- The Atlas of Finite Groups - Ten Years On , pp. 288 - 293Publisher: Cambridge University PressPrint publication year: 1998
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