Biset functors for finite groups / Serge Bouc

Auteur: Bouc, Serge (1955-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 1990Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, cop. 2010Description: 1 vol. (IX-299 p.) ; 24 cm ISBN: 9783642112966 ; br. ISSN: 0075-8434Résumé: 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. (Source : Springer).Bibliographie: Bibliogr. p. 293-295. Index. Sujets MSC: 20J15 Group theory and generalizations -- Connections with homological algebra and category theory -- Category of groups
19A22 K-theory -- Grothendieck groups and K0 -- Frobenius induction, Burnside and representation rings
20C15 Group theory and generalizations -- Representation theory of groups -- Ordinary representations and characters
20C20 Group theory and generalizations -- Representation theory of groups -- Modular representations and characters
En-ligne: Sommaire | Zentralblatt | MathSciNet
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Bibliogr. p. 293-295. Index

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. (Source : Springer)

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