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OverviewThis 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. Full Product DetailsAuthor: serge BoucPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2010 ed. Volume: 1990 Dimensions: Width: 15.50cm , Height: 1.60cm , Length: 23.50cm Weight: 0.990kg ISBN: 9783642112966ISBN 10: 364211296 Pages: 306 Publication Date: 11 March 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsExamples.- 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.ReviewsFrom the reviews: The theory of biset functors was developed to give a unified construction of the elementary operations of restriction, induction, inflation, deflation and transport by isomorphism. ! This volume gives an excellent introduction to the topic, which until now was only available in a series of research papers. ! The book can be read by graduate students with a good knowledge of algebra, but will also be a valuable source for researchers. (Robert Hartmann, Mathematical Reviews, Issue 2011 d) From the reviews: The theory of biset functors was developed to give a unified construction of the elementary operations of restriction, induction, inflation, deflation and transport by isomorphism. ... This volume gives an excellent introduction to the topic, which until now was only available in a series of research papers. ... The book can be read by graduate students with a good knowledge of algebra, but will also be a valuable source for researchers. (Robert Hartmann, Mathematical Reviews, Issue 2011 d) Author InformationTab Content 6Author Website:Countries AvailableAll regions |