03605nam 22006495 450 99646651690331620200704150247.01-280-39166-997866135695853-642-11297-810.1007/978-3-642-11297-3(CKB)2670000000010110(SSID)ssj0000449114(PQKBManifestationID)11323613(PQKBTitleCode)TC0000449114(PQKBWorkID)10392772(PQKB)11115013(DE-He213)978-3-642-11297-3(MiAaPQ)EBC3065081(PPN)149078641(EXLCZ)99267000000001011020100316d2010 u| 0engurnn|008mamaatxtccrBiset Functors for Finite Groups[electronic resource] /by serge Bouc1st ed. 2010.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2010.1 online resource (X, 306 p. 4 illus.) Lecture Notes in Mathematics,0075-8434 ;1990Bibliographic Level Mode of Issuance: Monograph3-642-11296-X Includes bibliographical references and index.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.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.Lecture Notes in Mathematics,0075-8434 ;1990Group theoryAlgebraic topologyK-theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019K-Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11086Group theory.Algebraic topology.K-theory.Group Theory and Generalizations.Algebraic Topology.K-Theory.512.220J1519A2220C1520G05mscBouc sergeauthttp://id.loc.gov/vocabulary/relators/aut61645BOOK996466516903316Biset functors for finite groups261777UNISA