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P-Automorphisms of Finite p-Groups / Evgenii I. Khukhro.

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Ideal for graduate students and researchers working in group theory and Lie rings.

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Khukhro, Evgenii I.
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 1998.
Series:London Mathematical Society lecture note series ; no. 246.
Subjects:
Automorphisms.
Finite groups.
Table of Contents:
  • Cover
  • Title
  • Copyright
  • Contents
  • Preface
  • Introduction
  • Chapter 1. Preliminaries
  • 1.1. Groups
  • 1.2. Rings and modules
  • 1.3. Algebraic systems, varieties and free objects
  • Exercises 1
  • Chapter 2. Automorphisms and their fixed points
  • 2.1. Semidirect products
  • 2.2. Automorphisms as linear transformations
  • 2.3. Induced automorphisms of factor- groups
  • Exercises 2
  • Chapter 3. Nilpotent and soluble groups
  • 3.1. The lower central series
  • 3.2. Nilpotent groups
  • 3.3. Soluble groups and varieties.
  • 3.4. Nilpotency criteria for soluble groups
  • Exercises 3
  • Chapter 4. Finite p-groups
  • 4.1. Basic properties
  • 4.2. A theorem of P. Hall
  • Exercises 4
  • Chapter 5. Lie rings
  • 5.1. Definitions and basic properties
  • 5.2. Nilpotent and soluble Lie rings
  • 5.3. Free Lie rings
  • Exercises 5
  • Chapter 6. Associated Lie rings
  • 6.1. Definition
  • 6.2. Basic properties
  • 6.3. Some applications
  • Exercises 6
  • Chapter 7. Regular automorphisms of Lie rings
  • 7.1. Graded Lie rings
  • 7.2. Combinatorial consequences
  • 7.3. Regular automorphisms
  • Exercises 7.
  • Chapter 8. Almost regular automorphism of order p:almost nilpotency of p-bounded class
  • Exercises 8
  • Chapter 9. The Baker-Hausdorff Formula and nilpotent Q-powered groups
  • 9.1. Free nilpotent groups
  • 9.2. The Baker-Hausdorff Formula
  • 9.3. Nilpotent Q-powered groups
  • Exercises 9
  • Chapter 10. The correspondences of A.I. Mal'cev and M. Lazard
  • 10.1. The Mal'cev Correspondence
  • 10.2. The Lazard Correspondence
  • Exercises 10
  • Chapter 11. Powerful p-groups
  • 11.1. Definitions and basic properties
  • 11.2. Finite p-groups of bounded rank
  • Exercises 11.
  • Chapter 12. Almost regular automorphism of order pn:almost solubility of pn-bounded derived length
  • 12.1. Uniformly powerful case
  • 12.2. Application of the Mal'cev Correspondence
  • 12.3. Almost solubility of pn-bounded derived length
  • Exercises 12
  • Chapter 13. p-Automorphisms with p fixed points
  • 13.1. Abelian p-groups
  • 13.2. Reduction to Lie rings
  • 13.3. The Lie ring theorem
  • Exercises 13
  • Chapter 14. Automorphism of order p with pm fixed points: almost nilpotency of m-bounded class
  • 14.1. Almost solubility of m-bounded derived length.
  • 14.2. Almost nilpotency of m-bounded class
  • Exercises 14
  • Bibliography
  • Index of names
  • Subject Index
  • List of symbols.

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