© 2010

Biset Functors for Finite Groups


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


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.


Prime Prime number algebra biset endopermutation functor group representation

Authors and affiliations

  1. 1.Fac. MathématiquesUniversité de PicardieAmiensFrance

Bibliographic information


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)