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Tables of Contents for Representations and Characters of Groups
Chapter/Section Title
Page #
Page Count
Preface
vii
Groups and homomorphisms
1
13
Vector spaces and linear transformations
14
16
Group representations
30
8
FG-modules
38
11
FG-submodules and reducibility
49
4
Group algebras
53
8
FG-homomorphisms
61
9
Maschke's Theorem
70
8
Schur's Lemma
78
11
Irreducible modules and the group algebra
89
6
More on the group algebra
95
9
Conjugacy classes
104
13
Characters
117
16
Inner products of characters
133
19
The number of irreducible characters
152
7
Character tables and orthogonality relations
159
9
Normal subgroups and lifted characters
168
11
Some elementary character tables
179
9
Tensor products
188
22
Restriction to a subgroup
210
14
Induced modules and characters
224
20
Algebraic integers
244
19
Real representations
263
20
Summary of properties of character tables
283
5
Characters of groups of order pq
288
10
Characters of some p-groups
298
13
Character table of the simple group of order 168
311
11
Character table of GL(2, q)
322
15
Permutations and characters
337
11
Applications to group theory
348
13
Burnside's Theorem
361
6
An application of representation theory to molecular vibration
367
30
Solutions to exercises
397
57
Bibliography
454
1
Index
455