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Blocks of Finite Groups

The Hyperfocal Subalgebra of a Block

  • Lluís Puig

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-v
  2. Lluís Puig
    Pages 1-6
  3. Lluís Puig
    Pages 7-18
  4. Lluís Puig
    Pages 31-39
  5. Lluís Puig
    Pages 41-51
  6. Lluís Puig
    Pages 65-70
  7. Lluís Puig
    Pages 71-83
  8. Lluís Puig
    Pages 99-119
  9. Lluís Puig
    Pages 121-133
  10. Lluís Puig
    Pages 135-147
  11. Lluís Puig
    Pages 163-178
  12. Lluís Puig
    Pages 179-192
  13. Back Matter
    Pages 209-215

About this book

Introduction

About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block.
But the main discovery of Brauer is perhaps the existence of families of infinitely many nonisomorphic groups having a "common block"; i.e., blocks having mutually isomorphic "source algebras".
In this book, based on a course given by the author at Wuhan University in 1999, all the concepts mentioned are introduced, and all the proofs are developed completely. Its main purpose is the proof of the existence and the uniqueness of the "hyperfocal subalgebra" in the source algebra. This result seems fundamental in block theory; for instance, the structure of the source algebra of a nilpotent block, an important fact in block theory, can be obtained as a corollary.

The exceptional layout of this bilingual edition featuring 2 columns per page (one English, one Chinese) sharing the displayed mathematical formulas is the joint achievement of the author and A. Arabia.

Keywords

Group algebra block hyperfocal algebra source algebra

Authors and affiliations

  • Lluís Puig
    • 1
  1. 1.Institut de Mathématiques de JussieuUniversité de Paris 7 — Denis DiderotParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-11256-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07802-6
  • Online ISBN 978-3-662-11256-4
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site