Biset functors for finite groups /

Biset functors for finite groups /

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Bibliographic Details
Author / Creator:	Bouc, Serge, 1955-
Imprint:	Heidelberg ; New York : Springer, ©2010.
Description:	1 online resource (ix, 299 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1990 Lecture notes in mathematics (Springer-Verlag) ; 1990.
Subject:	Functor theory. Finite groups. Finite groups. Functor theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11074478

Hidden Bibliographic Details
ISBN:	9783642112973 3642112978 9783642112966 364211296X
Notes:	Includes bibliographical references (pages 293-295) and index. Print version record.
Summary:	Annotation 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.
Other form:	Print version: Bouc, Serge, 1955- Biset functors for finite groups. Heidelberg ; New York : Springer, ©2010 9783642112966 364211296X

Table of Contents:

Examples
pt. 1. General properties. G-sets and (H, G)-bisets ; Biset functors ; Simple functors
pt. 2. Biset functors on replete subcategories. The Burnside functor ; Endomorphism algebras ; The functor CRC ; Tensor product and internal Hom
pt. 3. P-biset functors. Rational representations of p-groups ; P-biset functors ; Applications ; The Dade group.