Biset Functors for Finite Groups

  • Serge Bouc

Part of the Lecture Notes in Mathematics book series (LNM, volume 1990)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Serge Bouc
    Pages 1-11
  3. General Properties

    1. Front Matter
      Pages 14-14
    2. Serge Bouc
      Pages 15-40
    3. Serge Bouc
      Pages 41-51
    4. Serge Bouc
      Pages 53-72
  4. Biset Functors on Replete Subcategories

    1. Front Matter
      Pages 74-74
    2. Serge Bouc
      Pages 75-95
    3. Serge Bouc
      Pages 97-119
    4. Serge Bouc
      Pages 135-152
  5. p-Biset Functors

    1. Front Matter
      Pages 154-154
    2. Serge Bouc
      Pages 155-181
    3. Serge Bouc
      Pages 183-213
    4. Serge Bouc
      Pages 215-240
    5. Serge Bouc
      Pages 241-292
  6. Back Matter
    Pages 293-299

About this book

Introduction

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.

Keywords

Prime Prime number algebra biset endopermutation functor group representation

Authors and affiliations

  • Serge Bouc
    • 1
  1. 1.Fac. MathématiquesUniversité de PicardieAmiensFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-11297-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-11296-6
  • Online ISBN 978-3-642-11297-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site