CONTENTS
Introduction xi
CHAPTER I. Groups and Counting Principles 1
1 Groups 1
2 G-spaces 2
3 Direct and semidirect products 5
4 Finite groups of rotations 11
5 The Platonic groups 13
6 The Sylow theorems 16
7 Counting and group structure 18
CHAPTER II. Fundamentals of Group Representations 21
1 Definition and unitarity 21
2 Irreducibility and complete reduction 23
3 The group algebra and the regular representations 25
4 Schur's lemma 27
5 Tensor products 29
6 Complex conjugate representations; Quaternionic representations 30
7 One-dimensional representations 34
CHAPTER III. Abstract Theory of Representations of Finite Groups 35
1 Orthogonality relations and the first fundamental relation 36
2 Characters, class functions, and conjugacy classes 39
3 One-dimensional representations 42
4 The dimension theorem 43
5 The theorem of Frobenius and Schur 47
Appendix to III.5—Representations on real and quaternionic
vector spaces 50
6 Representations and group structure 55
7 Projections in the group algebra 56
8 Fourier analysis 57
9 Direct products 59
10 Restrictions 59
11 Subgroups of index 2 60
12 Examples 62
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