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p-Automorphisms of Finite p-Groups

p-Automorphisms of Finite p-Groups

£39.99

Part of London Mathematical Society Lecture Note Series

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

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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: 229 x 152 x 13 mm
    • weight: 0.34kg
    • 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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