The Jacobson Radical of Group Algebras, Volume 135

1st Edition

Authors: G. Karpilovsky
Hardcover ISBN: 9780444701909
eBook ISBN: 9780080872469
Imprint: North Holland
Published Date: 1st April 1987
Page Count: 531
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Table of Contents

Ring-Theoretic Background. Group Algebras and Their Modules. The Jacobson Radical of Group Algebras: Foundations of the Theory. Group Algebras of p-Groups over Fields of Characteristic p. The Jacobson Radical and Induced Modules. The Loewy Length of Projective Modules. The Nilpotency Index. Radicals of Blocks. Bibliography. Index.

Description

Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.

The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.


Details

No. of pages:
531
Language:
English
Copyright:
© North Holland 1987
Published:
Imprint:
North Holland
eBook ISBN:
9780080872469
Hardcover ISBN:
9780444701909

Reviews

Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results. The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.


About the Authors

G. Karpilovsky Author

Affiliations and Expertise

California State University, Department of Mathematics, Chico, CA, USA