Representations and Characters of Groups Book

	Preface
1	Groups and homomorphisms	1
2	Vector spaces and linear transformations	14
3	Group representations	30
4	FG-modules	38
5	FG-submodules and reducibility	49
6	Group algebras	53
7	FG-homomorphisms	61
8	Maschke's Theorem	70
9	Schur's Lemma	78
10	Irreducible modules and the group algebra	89
11	More on the group algebra	95
12	Conjugacy classes	104
13	Characters	117
14	Inner products of characters	133
15	The number of irreducible characters	152
16	Character tables and orthogonality relations	159
17	Normal subgroups and lifted characters	168
18	Some elementary character tables	179
19	Tensor products	188
20	Restriction to a subgroup	210
21	Induced modules and characters	224
22	Algebraic integers	244
23	Real representations	263
24	Summary of properties of character tables	283
25	Characters of groups of order pq	288
26	Characters of some p-groups	298
27	Character table of the simple group of order 168	311
28	Character table of GL(2, q)	322
29	Permutations and characters	337
30	Applications to group theory	348
31	Burnside's Theorem	361
32	An application of representation theory to molecular vibration	367
	Solutions to exercises	397
	Bibliography	454
	Index	455