Evgenii I. Khukhro

p-Automorphisms of Finite p-Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 13. Februar 1998
• Englisch
• ISBN-13: 9780511893421
• Artikelnr.: 38211211

Inhaltsangabe

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.