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Abstract Root Subgroups and Simple Groups of Lie-Type

  • Book
  • © 2001

Overview

Authors:
  1. Franz Georg Timmesfeld

    1. Mathematisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany

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Part of the book series: Monographs in Mathematics (MMA, volume 95)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Rank One Groups

    • Franz Georg Timmesfeld
    Pages 1-66

  3. Abstract Root Subgroups

    • Franz Georg Timmesfeld
    Pages 67-149

  4. Classification Theory

    • Franz Georg Timmesfeld
    Pages 151-256

  5. Root involutions

    • Franz Georg Timmesfeld
    Pages 257-312

  6. Applications

    • Franz Georg Timmesfeld
    Pages 313-371

  7. Back Matter

    Pages 373-389
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Keywords

About this book

It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson.

Reviews

"The book is well written: the style is concise but not hard and most of the book is not too difficult to read for a graduate student. Some parts of it are certainly suited for a class."

--Mathematical Reviews

Authors and Affiliations

  • Mathematisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany

    Franz Georg Timmesfeld

Bibliographic Information

  • Book Title: Abstract Root Subgroups and Simple Groups of Lie-Type

  • Authors: Franz Georg Timmesfeld

  • Series Title: Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7594-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 2001

  • Hardcover ISBN: 978-3-7643-6532-5Published: 01 August 2001

  • Softcover ISBN: 978-3-0348-7596-7Published: 12 June 2012

  • eBook ISBN: 978-3-0348-7594-3Published: 06 December 2012

  • Series ISSN: 1017-0480

  • Series E-ISSN: 2296-4886

  • Edition Number: 1

  • Number of Pages: XIII, 389

  • Topics: Group Theory and Generalizations

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