p-Automorphisms of Finite p-Groups
p-Automorphisms of Finite p-Groups
£46.99
GBPThis 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
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
Product details
February 1998Paperback
9780521597173
224 pages
228 × 153 × 14 mm
0.31kg
138 exercises
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.
