Advertisement

Twelve Sporadic Groups

  • Robert L. GriessJr.
Book

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

Table of contents

  1. Front Matter
    Pages I-4
  2. Robert L. Griess Jr.
    Pages 5-10
  3. Robert L. Griess Jr.
    Pages 11-23
  4. Robert L. Griess Jr.
    Pages 24-29
  5. Robert L. Griess Jr.
    Pages 30-35
  6. Robert L. Griess Jr.
    Pages 36-53
  7. Robert L. Griess Jr.
    Pages 54-75
  8. Robert L. Griess Jr.
    Pages 76-87
  9. Robert L. Griess Jr.
    Pages 88-94
  10. Robert L. Griess Jr.
    Pages 95-103
  11. Robert L. Griess Jr.
    Pages 146-153
  12. Back Matter
    Pages 154-169

About this book

Introduction

The finite simple groups are basic objects in algebra since many questions about general finite groups can be reduced to questions about the simple groups. Finite simple groups occur naturally in certain infinite families, but not so for all of them: the exceptions are called sporadic groups, a term used in the classic book of Burnside [Bur] to refer to the five Mathieu groups. There are twenty six sporadic groups, not definitively organized by any simple theme. The largest of these is the monster, the simple group of Fischer and Griess, and twenty of the sporadic groups are involved in the monster as subquotients. These twenty constitute the Happy Family, and they occur naturally in three generations. In this book, we treat the twelve sporadics in the first two generations. I like these twelve simple groups very much, so have chosen an exposition to appreciate their beauty, linger on details and develop unifying themes in their structure theory. Most of our book is accessible to someone with a basic graduate course in abstract algebra and a little experience with group theory, especially with permu­ tation groups and matrix groups. In fact, this book has been used as the basis for second-year graduate courses.

Keywords

Group theory Lattice algebra infinite families simple finite groups sporadic groups

Authors and affiliations

  • Robert L. GriessJr.
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03516-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08305-1
  • Online ISBN 978-3-662-03516-0
  • Series Print ISSN 1439-7382
  • Series Online ISSN 1439-7382
  • Buy this book on publisher's site