P-Automorphisms of Finite P-Groups

ISBN-13: 9780521597173 / Angielski / Miękka / 1998 / 224 str.

Evgenii I. Khukhro; E. I. Khukhro; N. J. Hitchin

Opis

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.

Recenzje

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

Spis treści

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.