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The Finite Simple Groups

  • Authors
  • Robert A. Wilson

Part of the Graduate Texts in Mathematics book series (GTM, volume 251)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Robert A. Wilson
    Pages 1-10
  3. Robert A. Wilson
    Pages 11-39
  4. Robert A. Wilson
    Pages 41-109
  5. Robert A. Wilson
    Pages 111-182
  6. Robert A. Wilson
    Pages 183-281
  7. Back Matter
    Pages 283-298

About this book

Introduction

The finite simple groups are the building blocks from which all the finite groups are made and as such they are objects of fundamental importance throughout mathematics. The classification of the finite simple groups was one of the great mathematical achievements of the twentieth century, yet these groups remain difficult to study which hinders applications of the classification.

This textbook brings the finite simple groups to life by giving concrete constructions of most of them, sufficient to illuminate their structure and permit real calculations both in the groups themselves and in the underlying geometrical or algebraic structures. This is the first time that all the finite simple groups have been treated together in this way and the book points out their connections, for example between exceptional behaviour of generic groups and the existence of sporadic groups, and discusses a number of new approaches to some of the groups. Many exercises of varying difficulty are provided.

The Finite Simple Groups is aimed at advanced undergraduate and graduate students in algebra as well as professional mathematicians and scientists who use groups and want to apply the knowledge which the classification has given us. The main prerequisite is an undergraduate course in group theory up to the level of Sylow’s theorems.

Keywords

Algebra Algebraic structure Alternating groups Group theory type groups Simple groups Sporadic groups

Bibliographic information