ProofWiki:Books/John F. Humphreys/A Course in Group Theory

John F. Humphreys: A Course in Group Theory

Published 1996, Oxford University Press.

ISBN 0-19-853459-0

Subject Matter

• Group Theory

Contents

Preface (Liverpool, January 1996)

1 Definitions and examples

2 Maps and relations on sets

3 Elementary consequences of the definitions

4 Subgroups

5 Cosets and Lagrange's Theorem

6 Error-correcting codes

7 Normal subgroups and quotient groups

8 The Homomorphism Theorem

9 Permutations

10 The Orbit-Stabiliser Theorem

11 The Sylow Theorems

12 Applications of Sylow theory

13 Direct products

14 The classification of finite abelian groups

15 The Jordan–Hölder Theorem

16 Composition factors and chief factors

17 Soluble groups

18 Examples of soluble groups

19 Semidirect products and wreath products

20 Extensions

21 Central and cyclic extensions

22 Groups with at most 31 elements

23 The projective special linear groups

24 The Mathieu groups

25 The classification of finite simple groups

25.1 The classical groups

25.1.1 The projective special linear groups

25.1.2 The unitary groups

25.1.3 The symplectic groups

25.1.4 The orthogonal groups

25.2 Groups of Lie type

25.3 The sporadic groups

A Prerequisites from number theory and linear algebra

A.1 Number theory

A.2 Linear algebra and determinants

B Groups of order < 32

C Solutions to exercises

Bibliography

Index