P-automorphisms of finite p-groups / E.I. Khukhro.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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

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.