Biset functors for finite groups
Author(s)
Bibliographic Information
Biset functors for finite groups
（Lecture notes in mathematics, 1990）
Springer, c2010
Available at / 55 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1990200017822148
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Note
Includes bibliographical references (p. 293-295) and index
Description and Table of Contents
Description
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.
Table of Contents
Examples.- General properties.- -Sets and (, )-Bisets.- Biset Functors.- Simple Functors.- Biset functors on replete subcategories.- The Burnside Functor.- Endomorphism Algebras.- The Functor.- Tensor Product and Internal Hom.- p-biset functors.- Rational Representations of -Groups.- -Biset Functors.- Applications.- The Dade Group.
by "Nielsen BookData"