Representation Theory of Finite Groups: Algebra and Arithmetic

By: Steven H. Weintraub

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Hardcover | 1 January 2003

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232 Pages

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26.1 x 18.4 x 1.6

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"The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference."--BOOK JACKET. Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

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Preface
Introduction	p. 1
Semisimple Rings and Modules	p. 7
Basic Notions	p. 7
Structure Theorems	p. 9
Idempotents and Blocks	p. 21
Behavior under Field Extensions	p. 27
Theorems of Burnside and Frobenius-Schur	p. 38
Semisimple Group Representations	p. 41
Examples and General Results	p. 41
Representations of Abelian Groups	p. 53
Decomposition of the Regular Representation	p. 56
Applications of Frobenius's Theorem	p. 59
Characters	p. 64
Idempotents and their Uses	p. 81
Subfields of the Complex Numbers	p. 86
Fields of Positive Characteristic	p. 96
Induced Representations and Applications	p. 99
Induced Representations	p. 99
Mackey's Theorem	p. 120
Permutation Representations	p. 128
M-groups	p. 139
Theorems of Artin and Brauer	p. 142
Degrees of Irreducible Representations	p. 152
Introduction to Modular Representations	p. 155
General Rings and Modules	p. 161
Jordan-Holder and Krull-Schmidt Theorems	p. 161
The Jacobson Radical	p. 170
Rings of Finite Length	p. 172
Finite-dimensional Algebras	p. 181
Modular Group Representations	p. 187
General Results	p. 187
Characters and Brauer Characters	p. 193
Examples	p. 196
Some Useful Results	p. 203
Bibliography	p. 209
Index	p. 211
Table of Contents provided by Blackwell. All Rights Reserved.

Representation Theory of Finite Groups: Algebra and Arithmetic

At a Glance

Hardcover

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