Clifford Theory for Group Representations

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Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products. The purpose of this monograph is to tie together various threads of the development in order to give a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, i.e. familiarity with basic ring-theoretic, number-theoretic and group-theoretic concepts, and an understanding of elementary properties of modules, tensor products and fields.

Author(s): Leopoldo Nachbin and Gregory Karpilovsky (Eds.)
Series: Notas de matematica 125 North-Holland mathematics studies 156
Publisher: North-Holland
Year: 1989

Language: English
Pages: ii-viii, 1-364
City: Amsterdam; New York :, New York, N.Y., U.S.A

Content:
Edited by
Pages ii-iii

Copyright page
Page iv

Preface
Pages vii-viii
Gregory Karpilovsky

Chapter 1 Preliminaries
Pages 1-66

Chapter 2 Restriction to Normal Subgroups
Pages 67-167

Chapter 3 Induction and Extension from Normal Subgroups
Pages 169-342

Bibliography
Pages 343-354

National
Pages 355-358

Index
Pages 359-364