© 2014

Blocks of Finite Groups and Their Invariants


Part of the Lecture Notes in Mathematics book series (LNM, volume 2127)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Fundamentals

    1. Front Matter
      Pages 1-1
    2. Benjamin Sambale
      Pages 3-17
    3. Benjamin Sambale
      Pages 19-22
  3. General Results and Methods

    1. Front Matter
      Pages 23-23
    2. Benjamin Sambale
      Pages 25-32
    3. Benjamin Sambale
      Pages 33-46
    4. Benjamin Sambale
      Pages 47-61
  4. Applications

    1. Front Matter
      Pages 79-79
    2. Benjamin Sambale
      Pages 81-94
    3. Benjamin Sambale
      Pages 95-125
    4. Benjamin Sambale
      Pages 127-157
    5. Benjamin Sambale
      Pages 159-165
    6. Benjamin Sambale
      Pages 167-179
    7. Benjamin Sambale
      Pages 181-203
    8. Benjamin Sambale
      Pages 205-217
    9. Benjamin Sambale
      Pages 219-227
  5. Back Matter
    Pages 229-246

About this book


Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.


20C15,20C20,20C40 Blocks of finite groups Defect groups Open conjectures Representation theory

Authors and affiliations

  1. 1.Institut für MathematikFriedrich-Schiller-Universität JenaJenaGermany

Bibliographic information

  • Book Title Blocks of Finite Groups and Their Invariants
  • Authors Benjamin Sambale
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-12005-8
  • eBook ISBN 978-3-319-12006-5
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XIII, 243
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Group Theory and Generalizations
  • Buy this book on publisher's site


“It gives an excellent survey of the current state of knowledge with regards to the precise determination of the numerical invariants of blocks with a given defect group … . The book is a treasure trove of theorems and useful tables, and uses a wide variety of techniques, including the classification of finite simple groups and the GAP computer algebra package. It is the progress made without use of the classification, however, which is particularly impressive.” (Charles W. Eaton, Mathematical Reviews, February, 2016)