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Local Analysis for the Odd Order Theorem

Local Analysis for the Odd Order Theorem


Part of London Mathematical Society Lecture Note Series

  • Date Published: May 1995
  • availability: Available
  • format: Paperback
  • isbn: 9780521457163

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About the Authors
  • In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit–Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory.

    • The first exposition in book form of a famous mathematical result
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    Reviews & endorsements

    'This book is written well … the authors have succeeded both in simplifying the proof of the Odd Order Theorem and in making it accessible to a wider audience.' Paul Flavell, Bulletin of the London Mathematical Society

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    Product details

    • Date Published: May 1995
    • format: Paperback
    • isbn: 9780521457163
    • length: 188 pages
    • dimensions: 229 x 152 x 11 mm
    • weight: 0.28kg
    • availability: Available
  • Table of Contents

    Part I. Preliminary Results:
    1. Notation and elementary properties of solvable groups
    2. General results on representations
    3. Actions of Frobenius groups and related results
    4. p-Groups of small rank
    5. Narrow p-groups
    6. Additional results
    Part II. The Uniqueness Theorem:
    7. The transitivity theorem
    8. The fitting subgroup of a maximal subgroup
    9. The uniqueness theorem
    Part III. Maximal Subgroups:
    10. The subgroups Ma and Me
    11. Exceptional maximal subgroups
    12. The subgroup E
    13. Prime action
    Part IV. The Family of All Maximal Subgroups of G:
    14. Maximal subgroups of type p and counting arguments
    15. The subgroup Mf
    16. The main results
    Prerequisites and p-stability.

  • Authors

    Helmut Bender, Christian-Albrechts Universität zu Kiel, Germany

    George Glauberman, University of Chicago

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