Groups, Combinatorics & Geometry: Durham 2001

by Ivanov, A. A.; Liebeck, Martin W.; Saxl, Jan

• ISBN13: 9789812383129
• ISBN10: 9812383123
• Format: Hardcover
• Copyright: 2003-03-01
• Publisher: World Scientific Pub Co Inc

Summary

cOver the past 20 years, the theory of groups -- in particular simple groups, finite and algebraic -- has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups.This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications.

Table of Contents

Preface
List of authors and addresses
Classification of simple K -groups of finite Morley rank and even type: geometric aspects	p. 1
Curtis-Phan-Tits theory	p. 13
Representation theory of symmetric groups and their double covers	p. 31
Coherent configurations, association schemes and permutation groups	p. 55
Mathematical developments from the analysis of riffle shuffling	p. 73
Derangements in simple and primitive groups	p. 99
Computing with matrix groups	p. 123
A survey of maximal subgroups of exceptional groups of Lie type	p. 139
Bases of primitive permutation groups	p. 147
Finite groups of local characteristic p: an overview	p. 155
Modular subgroup arithmetic	p. 193
Counting nets in the monster	p. 227
Overgroups of finite quasiprimitive permutation groups	p. 233
Old groups can learn new tricks	p. 243
Shadows of elements, solvability of finite quotients and the Margulis-Platonov conjecture	p. 257
Applications of random generation to residual properties of some infinite groups	p. 269
Low dimensional representations of finite quasisimple groups	p. 277
Structure and presentations of Lie-type groups	p. 295
Vertex stabilizers of locally projective groups of automorphisms of graphs: a summary	p. 313
Computing in the monster	p. 327
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