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Groups and Representations : Graduate Texts in Mathematics - J. L. Alperin

Groups and Representations

Graduate Texts in Mathematics

Paperback

Published: 11th September 1995
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This book provides a concise treatment of some topics from group theory and representation theory, suitable 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 will enable graduate students from every mathematical field, as well as advanced 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.

Preface
Rudiments of Group Theoryp. 1
Reviewp. 1
Automorphismsp. 14
Group Actionsp. 27
The General Linear Groupp. 39
Basic Structurep. 39
Parabolic Subgroupsp. 49
The Special Linear Groupp. 56
Local Structurep. 63
Sylow's Theoremp. 63
Finite p-groupsp. 72
The Schur-Zassenhaus Theoremp. 81
Normal Structurep. 89
Composition Seriesp. 89
Solvable Groupsp. 95
Semisimple Algebrasp. 107
Modules and Representationsp. 107
Wedderburn Theoryp. 120
Group Representationsp. 137
Charactersp. 137
The Character Tablep. 146
Inductionp. 164
Appendix: Algebraic Integers and Charactersp. 179
Bibliographyp. 185
List of Notationp. 187
Indexp. 191
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387945262
ISBN-10: 0387945261
Series: Graduate Texts in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 196
Published: 11th September 1995
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 1.5
Weight (kg): 0.25