The Atlas of Finite Groups - Ten Years On

by Edited by R. T. Curtis , R. A. Wilson

• ISBN13: 9780521575874
• ISBN10: 0521575877
• Format: Paperback
• Copyright: 1998-06-28
• Publisher: Cambridge University Press

Summary

The Atlas of Finite Groups by J. H. Conway, R. A. Parker, S. P. Norton and the editors of this book, was published in 1985, and has proved itself to be an indispensable tool to all researchers in group theory and many related areas. The present book is the proceedings of a conference organised to mark the 10th anniversary of the publication of the Atlas, and contains twenty articles by leading experts in the field, covering many aspects of group theory and its applications. There are surveys on recent developments, expository articles, and research papers, as well as a historical article on the development of the Atlas project since 1970. The book emphasises recent advances in group theory and applications which have been stimulated by the comprehensive collection of information contained in the Atlas, and covers both theoretical and computational aspects of finite groups, modular representation theory, presentations, and applications to the study of surfaces.

Table of Contents

Introduction	vii	(2)
Addresses of registered participants	ix	(4)
Addresses of non-participating authors	xiii	(1)
Programme of lectures	xiv	(2)
Conference photograph and key	xvi
C.M. Campbell
G. Havas
S.A. Linton
E.F. Robertson
Symmetric presentations and orthogonal groups	1	(10)
F. Celler
C.R. Leedham-Green
A constructive recognition algorithm for the special linear group	11	(16)
J.H. Conway
C.S. Simons
Relations in M(666)	27	(12)
R.T. Curtis
A survey of symmetric generation of sporadic simple groups	39	(19)
G. Hiss
Harish-Chandra theory, q-Schur algebras, and decomposition matrices for finite classical groups	58	(16)
D.F. Holt
The Meataxe as a tool in computational group theory	74	(8)
J.F. Humphreys
Branching rules for modular projective representations of the symmetric groups	82	(8)
G.A. Jones
Characters and surfaces: a survey	90	(29)
W. Kimmerle
On the characterization of finite groups by characters	119	(20)
A.S. Kondratiev
Finite linear groups of small degree	139	(10)
W. Lempken
C. Parker
P. Rowley
Minimal parabolic systems for the symmetric and alternating groups	149	(14)
M.W. Liebeck
A. Shalev
Probabilistic methods in the generation of finite simple groups	163	(11)
K. Lux
M. Wiegelmann
Condensing tensor product modules	174	(17)
V.D. Mazurov
V.I. Zenkov
Intersections of Sylow subgroups in finite groups	191	(7)
S.P. Norton
Anatomy of the Monster. I	198	(17)
R.A. Parker
An integral `Meat-axe'	215	(14)
W. Plesken
Finite rational matrix groups: a survey	229	(20)
P. Rowley
Chamber graphs of sporadic group geometries	249	(12)
R.A. Wilson
An Atlas of sporadic group representations	261	(13)
F. Zara
Presentations of reductive Fischer groups	274	(14)
J.H. Conway
R.T. Curtis
R.A. Wilson
A brief history of the ATLAS	288