Now in its second edition, this text provides a modern introduction to the representation theory of finite groups. The authors have revised the popular first edition and added a considerable amount of new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all simple groups of order less than 1000.

Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book. This will be ideal as a text for a course in representation theory, and in view of the applications of the subject, will be of interest to mathematicians, chemists and physicists alike.

Preface

1 Groups and homomorphisms

2 Vector spaces and linear transformations

3 Group representations

4 FG-modules

5 FG-submodules and reducibility

6 Group algebras

7 FG-homomorphisms

8 Maschke's Theorem

9 Schur's Lemma

10 Irreducible modules and the group algebra

11 More on the group algebra

12 Conjugacy classes

13 Characters

14 Inner products of characters

15 The number of irreducible characters

16 Character tables and orthogonality relations

17 Normal subgroups and lifted characters

18 Some elementary character tables

19 Tensor products

20 Restriction to a subgroup

21 Induced modules and characters

22 Algebraic integers

23 Real representations

24 Summary of properties of character tables

25 Characters of groups of order pq

26 Characters of some p-groups

27 Character table of the simple group of order 168

28 Character table of GL(2, q)

29 Permutations and characters

30 Applications to group theory

31 Burnside's Theorem

32 An application of representation theory to molecular vibration

Solutions to exercises

Bibliography

Index