Front Cover 1
Representation Theory of Finite Groups 4
Copyright Page 5
Table of Contents 8
Chapter I. Foundations 12
1. Introduction 12
2. Group Characters 23
3. Representation Modules 24
4. Application of Ideas and Results from Group Theory 28
5. The Regular Representation 34
Chapter II. Representation Theory of Rings with Identity 39
6. Some Fundamental Lemmas 39
7. The Principal Indecomposable Representations 45
8. The Radical of a Ring 48
9. Semisimple Rings 51
10. The Wedderburn Structure Theorems for Semisimple Rings 53
11. Intertwining Numbers 58
12. Multiplicities of the Indecomposable Components 
64 
13. The Generalized Burnside Theorem 66
Chapter III. The Representation Theory of Finite Groups 69
14. The Group Algebra 69
15. The Regular Representation of a Group 71
16. Semisimplicity of the Group Algebra 71
17. The Center of the Group Algebra 75
18. The Number of Inequivalent Irreducible Representations 76
19. Relations on the Irreducible Characters 78
20. The Module of Characters over the Integers 82
21. The Kronecker Product of Two Representations 83
22. Linear Characters 87
23. Induced Representations and Induced Characters 88
Chapter IV. Applications of the Theory of Characters 96
24. Algebraic Numbers 96
25. Some Results from the Theory of Characters 98
26. Normal Subgroups and the Character Table 103
27. Some Classical Theorems 105
Chapter V. The Construction of Irreducible Representations 110
28. Primitive Idempotents 110
29. Some examples of Group Representations 116
Chapter VI. Modular Representations 131
30. General Remarks 131
31. p-Regular Elements of a Finite Group 133
32. Conditions for Two Representations to Have the Same Composition Factors 136
33. The Brauer Characters 139
34. Integral Representations 141
35. Ordinary and Modular Representations of Algebras 145
36. p-Adic Fields 148
37. Algebras over a p-Aaic Field 159
38. A Connection between the Intertwining Numbers 168
39. Modular Representations of Groups 170
40. Cartan Invariants and Decomposition Numbers 172
41. Character Relations 175
42. Modular Orthogonality Relations 180
Appendix 184
1. Groups 184
2. Rings, Ideals, and Fields 187
BIBLIOGRAPHY 191
SUBJECT INDEX 194