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Theory of Finite Simple Groups

Theory of Finite Simple Groups

Part of New Mathematical Monographs

  • Date Published: September 2006
  • availability: Unavailable - out of print
  • format: Mixed media product
  • isbn: 9780521866255

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  • This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. It presents self-contained proofs of classical and new group order formulas, and a new structure theorem for abstract finite simple groups. This, and the famous Brauer-Fowler theorem, provides the theoretical background for the author's algorithm which constructs all finite simple groups G having a 2-central involution z with a given centralizer CG(z)=H. The methods presented are designed for the construction of matrix representations, permutation representations and character tables of large finite groups. The author constructs all the simple satellites of the known simple groups that are not uniquely determined by a given centralizer H. Uniform existence and uniqueness proofs are given for the modern sporadic simple groups discovered by Janko, Higman and Sims, Harada, and Thompson. This latter result proves a long standing open problem in the theory. The experimental results (courtesy of M. Weller) for Chapter 12 are documented in the accompanying DVD.

    • Provides a new theoretical and algorithmic approach to the study of finite simple groups
    • Presents new algorithms for the construction of concrete character tables of arbitrary finite groups and shows how they can be used to provide uniform existence and uniqueness proofs
    • The accompanying DVD contains a large amount of experimental data
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    Reviews & endorsements

    'The approach described and advocated by Michler in this book is remarkable in that it offers a uniform method that can, in principle, be used to prove computationally the existence and uniqueness of almost all the sporadic simple groups.' Bulletin of the American Mathematical Society

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    Product details

    • Date Published: September 2006
    • format: Mixed media product
    • isbn: 9780521866255
    • length: 614 pages
    • dimensions: 235 x 161 x 39 mm
    • weight: 1.049kg
    • contains: 200 tables
    • availability: Unavailable - out of print
  • Table of Contents

    Introduction
    1. Prerequisites from group theory
    2. Group representations and character theory
    3. Modular representation theory
    4. Group order formulas and structure theorem
    5. Permutation representations
    6. Concrete character tables of matrix groups
    7. Methods for constructing finite simple groups
    8. Finite simple groups with proper satellites
    9. Janko group J1
    10. Higman-Sims group HS
    11. Harada group Ha
    9. Thompson group Th
    Bibliography
    List of symbols
    Index.

  • Author

    Gerhard O. Michler, Cornell University, New York
    Gerhard Michler is an Emeritus Professor of the Institute of Experimental Mathematics at the Univerity of Duisburg-Essen

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