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Clifford theory for group representations
Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.
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.
Front Cover; Clifford Theory for Group Representations; Copyright Page; Preface; Contents; Chapter 1. Preliminaries; Chapter 2. Restriction to normal subgroups; Chapter 3. Induction and extension from normal subgroups; Bibliography; Notation; Index.
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Includes bibliographical references (pages 343-354) and index.
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., ©1989
Notas de matemática (Rio de Janeiro, Brazil) ; no. 125
119949:123203 Elsevier Science & Technology