Groups, Combinatorics And Geometry

DURHAM 2001

Alexander Anatolievich Ivanov, Martin W Liebeck, Jan Saxl

• Publisher: World Scientific
• Year: 2003
• Print ISBN:
  9789812383129
  9789812383129
• eBook ISBN:
  9789812564481
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Over 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
• CONTENTS
• List of authors and addresses
• Classification of Simple K*-Groups of Finite Morley Rank and Even Type: Geometric Aspects
• Curtis-Phan-Tits Theory
• REPRESENTATION THEORY OF SYMMETRIC GROUPS AND THEIR DOUBLE COVERS
• Coherent configurations, association schemes and permutation groups
• MATHEMATICAL DEVELOPMENTS FROM THE ANALYSIS OF RIFFLE SHUFFLING
• DERANGEMENTS IN SIMPLE AND PRIMITIVE GROUPS
• Computing with matrix groups*
• A survey of maximal subgroups of exceptional groups of Lie type
• Bases of primitive permutation groups
• Finite groups of local characteristic p An Overview
• Modular subgroup arithmetic
• Counting Nets in the Monster
• Overgroups of finite quasiprimitive permutation groups.
• Old groups can learn new tricks
• SHADOWS OF ELEMENTS, SOLVABILITY OF FINITE QUOTIENTS AND THE MARGULIS-PLATONOV CONJECTURE
• Applications of random generation to residual properties of some infinite groups
• LOW DIMENSIONAL REPRESENTATIONS OF FINITE QUASISIMPLE GROUPS
• STRUCTURE AND PRESENTATIONS OF LIE-TYPE GROUPS
• Vertex stabilizers of locally projective groups of automorphisms of graphs. A summary
• Computing in the Monster
• References