Gregory Karpilovsky (Eds.)9780444884145, 0444884149
In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations. This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area. After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings. |
Table of contents :
Content:
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Page iii Copyright page
Page iv Dedication
Page v Preface
Pages vii-viii Chapter 1 Preliminaries
Pages 1-44 Chapter 2 General properties of induced modules
Pages 45-129 Chapter 3 Induction from normal subgroups
Pages 131-272 Chapter 4 Projective summands of induced modules
Pages 273-297 Chapter 5 Green theory
Pages 299-340 Chapter 6 Simple induction and restriction pairs
Pages 341-382 Chapter 7 Permutation modules
Pages 383-458 Chapter 8 Permutation lattices
Pages 459-498 Bibliography
Pages 499-510 Notation
Pages 511-515 Index
Pages 516-520 |
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