Groups and Characters / Edition 1

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A lively and thorough textbook for graduate courses and general reference that illuminates the interdependence between group theory and representative/character theory. It includes an entire chapter of challenging and fully detailed examples, and there are exercises throughout the text that help readers prove for themselves its well-articulated points.
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Editorial Reviews

A textbook for a graduate mathematics course of one or two semesters. Combines group and character theory, with a focus on finite groups, and includes some computational aspects. Readers are assumed to have completed a graduate-level course in abstract algebra and have a reasonable facility with linear algebra. Also suitable as a reference for chemists, physicists, and crystallographers. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Meet the Author

LARRY C. GROVE is Professor of Mathematics at the University of Arizona He is the author of Algebra and coauthor of Finite Reflection Groups.
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Table of Contents

1 Preliminaries
1.1 Some Notation and Generalities 1
1.2 Permutation Actions 3
1.3 Coset Enumeration 9
1.4 Semidirect Products 13
1.5 Wreath Products 14
1.6 Transitivity and Primitivity 16
1.7 Some Linear Algebra 20
2 Some Groups
2.1 Aut(Z[subscript n]) 27
2.2 Metacyclic Groups 29
2.3 Sylow Subgroups of Symmetric Groups 30
2.4 Affine Groups of Fields 32
2.5 Finite Groups in 2 and 3 Dimensions 33
2.6 Some Linear Groups 39
2.7 Mathieu Groups 46
2.8 Symplectic Groups 52
3 Counting with Groups
3.1 Fixed Points and Orbits 61
3.2 The Cycle Index 64
3.3 Enumeration 68
3.4 Generating Functions 73
3.5 The Petersen Graph 75
4 Transfer and Splitting
4.1 Transfer and Normal Complements 77
4.2 Hall Subgroups 84
4.3 Mostly p-groups 89
5 Representations and Characters
5.1 Representations 97
5.2 Characters 105
5.3 Contragredients and Products 121
6 Induction and Restriction
6.1 Modules 127
6.2 Induction 128
6.3 Normal Subgroups and Clifford Theory 136
6.4 Mackey Theorems 142
6.5 Brauer Theorems 147
7 Computing Character Tables
7.1 Burnside 151
7.2 Dixon 154
7.3 Schneider 158
8 Characters of S[subscript n] and A[subscript n]
8.1 Symmetric Groups 161
8.2 Alternating Groups 168
9 Frobenius Groups
9.1 Frobenius Groups and Their Characters 171
9.2 Structure of Frobenius Groups 176
10 Splitting Fields
10.1 Splitting 183
10.2 The Schur Index 184
10.3 R versus C 190
Bibliography 203
Index 209
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