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Nilpotent Groups and their Automorphisms : De Gruyter Expositions in Mathematics - Evgenii I. Khukhro

Nilpotent Groups and their Automorphisms

De Gruyter Expositions in Mathematics

Hardcover

Published: 1st April 1993
For Ages: 22+ years old
Ships: 7 to 10 business days
7 to 10 business days
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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2018)
Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Botjan Gabrovek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Notation
Preface
Linear Methodsp. 1
Preliminariesp. 3
Groups
Rings and modules
Lie rings
Mappings, homomorphisms, automorphisms
Group actions on a set
Fixed points of automorphisms
The Jordan normal form of a linear transformation of finite order
Varieties and free groups
Groups with operators
Higman's Lemma
Nilpotent groupsp. 30
Commutators and commutator subgroups
Definitions and basic properties of nilpotent groups
Some sufficient conditions for soluble groups to be nilpotent
The Schur-Baer Theorem and its converses
Lower central series. Isolators
Nilpotent groups without torsion
Basic commutators and the collecting process
Finite p-groups
Associated Lie ringsp. 70
Results on Lie rings analogous to theorems about groups
Constructing a Lie ring from a group
The Lie ring of a group of prime exponent
The nilpotency of soluble Lie rings satisfying the Engel condition
Automorphismsp. 85
Lie rings admitting automorphisms with few fixed pointsp. 87
Extending the ground ring
Regular automorphisms of soluble Lie rings
Regular automorphisms of Lie rings
Almost regular automorphisms of prime order
Comments
Nilpotent groups admitting automorphisms of prime order with few fixed pointsp. 121
Regular automorphisms of prime order
Nilpotent p-groups with automorphisms of order p
Nilpotent groups with an almost regular automorphism of prime order
Comments
Nilpotency in varieties of groups with operatorsp. 155
Preliminary lemmas
A nilpotency theorem
A local nilpotency theorem
Corollaries
Comments
Splitting automorphisms of prime order and finite p-groups admitting a partitionp. 180
The connection between splitting automorphisms of prime order and finite p-groups admitting a partition
The Restricted Burnside Problem for groups with a splitting automorphism of prime order
The structure of finite p-groups admitting a partition and a positive solution of the Hughes problem
Bounding the index of the Hughes subgroup
Comments
Nilpotent p-groups admitting automorphisms of order p[superscript k] with few fixed pointsp. 226
An application of the Mal'cev correspondence
Powerful p-groups
A weak bound for the derived length
A strong bound for the derived length of a subgroup of bounded index
Referencesp. 240
Index of namesp. 248
Subject indexp. 250
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110136722
ISBN-10: 3110136724
Series: De Gruyter Expositions in Mathematics
Audience: Professional
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 265
Published: 1st April 1993
Publisher: De Gruyter
Country of Publication: DE
Dimensions (cm): 23.0 x 15.5  x 1.91
Weight (kg): 0.6