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p-Automorphisms of Finite p-Groups : London Mathematical Society Lecture Note Series - Evgenii I. Khukhro

p-Automorphisms of Finite p-Groups

London Mathematical Society Lecture Note Series

Paperback

Published: 27th April 1998
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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.

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

Preface
Introduction
Preliminaries
Automorphisms and their fixed points
Nilpotent and soluble groups
Finite p-groups
Lie rings
Associated Lie rings
Regular automorphisms of Lie rings
Almost regular automorphism of order p: almost nilpotency of p-bounded class
The Baker-Hausdorff formula and nilpotent Q-powered groups
The correspondences of
Powerful p-groups
Almost regular automorphism of order p^n: almost solubility of p^n-bounded derived length
p-Automorphisms with p fixed points
Automorphism of order p with p^m fixed points: almost nilpotency of m-bounded class
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521597173
ISBN-10: 052159717X
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 224
Published: 27th April 1998
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.3
Weight (kg): 0.34