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p-Automorphisms of Finite p-Groups

p-Automorphisms of Finite p-Groups

$59.99 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: February 1998
  • availability: Available
  • format: Paperback
  • isbn: 9780521597173

$ 59.99 (C)
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  • This book provides a detailed but concise account of the theory of structure of finite p-groups admitting p-automorphisms with few fixed points. The relevant preliminary material on Lie rings is introduced and the main theorems of the book on the solubility of finite p-groups are then presented. The proofs involve notions such as viewing automorphisms as linear transformations, associated Lie rings, powerful p-groups, and the correspondences of A.I. Mal'cev and M. Lazard given by the Baker-Hausdorff formula. Many exercises are included. This book is suitable for graduate students and researchers working in the fields of group theory and Lie rings.

    • Contains introductory material
    • Includes over 100 exercises
    • Very affordable paperback in highly respected series
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    Reviews & endorsements

    'This is a beautiful book. … this book is a delightful introduction to very general techniques in group theory.' Bulletin of the London Mathmatical Society

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    Product details

    • Date Published: February 1998
    • format: Paperback
    • isbn: 9780521597173
    • length: 224 pages
    • dimensions: 228 x 153 x 14 mm
    • weight: 0.31kg
    • contains: 138 exercises
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    1. Preliminaries
    2. Automorphisms and their fixed points
    3. Nilpotent and soluble groups
    4. Finite p-groups
    5. Lie rings
    6. Associated Lie rings
    7. Regular automorphisms of Lie rings
    8. Almost regular automorphism of order p: almost nilpotency of p-bounded class
    9. The Baker–Hausdorff formula and nilpotent Q-powered groups
    10. The correspondences of A.I. Mal'cev and M. Lazard
    11. Powerful p-groups
    12. Almost regular automorphism of order p^n: almost solubility of p^n-bounded derived length
    13. p-Automorphisms with p fixed points
    14. Automorphism of order p with p^m fixed points: almost nilpotency of m-bounded class
    Bibliography
    Index.

  • Author

    Evgenii I. Khukhro, Siberian Division of the Russian Academy of Sciences

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