Groups and Representations

By: J.L. Alperin, Rowen B. Bell

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212 Pages

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24.77 x 16.51 x 1.91

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The aim of this text is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book should enable graduate students from every mathematical field, as well as strong undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics.

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Preface
Rudiments of Group Theory	p. 1
Review	p. 1
Automorphisms	p. 14
Group Actions	p. 27
The General Linear Group	p. 39
Basic Structure	p. 39
Parabolic Subgroups	p. 49
The Special Linear Group	p. 56
Local Structure	p. 63
Sylow's Theorem	p. 63
Finite p-groups	p. 72
The Schur-Zassenhaus Theorem	p. 81
Normal Structure	p. 89
Composition Series	p. 89
Solvable Groups	p. 95
Semisimple Algebras	p. 107
Modules and Representations	p. 107
Wedderburn Theory	p. 120
Group Representations	p. 137
Characters	p. 137
The Character Table	p. 146
Induction	p. 164
Appendix: Algebraic Integers and Characters	p. 179
Bibliography	p. 185
List of Notation	p. 187
Index	p. 191
Table of Contents provided by Blackwell. All Rights Reserved.

Groups and Representations

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Hardcover

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