p-Automorphisms of Finite p-Groups
Part of London Mathematical Society Lecture Note Series
- Author: Evgenii I. Khukhro, Siberian Division of the Russian Academy of Sciences
- 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.
Read more- Contains introductory material
- Includes over 100 exercises
- Very affordable paperback in highly respected series
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'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.
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