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.

Author: Evgenii I. Khukhro

Publisher: Walter de Gruyter

ISBN: 9783110846218

Category: Mathematics

Page: 266

View: 654

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics 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 wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

For each t D 1; :::; n; there may be several distinct orderings. ... such ordering,
there are choices for n ! t v1 ; :::; vt; and thus n t actual sequences of 's satisfying
this specific ordering. ... E.I. Khukhro, Nilpotent Groups and Their Automorphisms.

Author: Anthony E. Clement

Publisher: Birkhäuser

ISBN: 9783319662138

Category: Mathematics

Page: 307

View: 729

This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.

... nilpotent groups, Amer. Math. Soc., Providence, R.I. Bourbaki N. [1980] Lie
groups and algebras, Chapters 1-3, Springer, Berlin et al. ... Khukhro E.I. [1993b] Nilpotent groups and their automorphisms, de Gruyter, Berlin. Kostrikin A. I. [1986
] ...

Author: Evgenii I. Khukhro

Publisher: Cambridge University Press

ISBN: 052159717X

Category: Mathematics

Page: 204

View: 106

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

[42] B. Hartley, Topics in the Theory of Nilpotent Groups, in: Group Theory —
Essays for Philip Hall, eds: K.W. ... [57] E.I. Khukhro, Nilpotent Groups and their Automorphisms, de Gruyter, Berlin, [58] E.I. Khukhro, p-Automorphisms of Finite ...

Author: Marcus du Sautoy

Publisher: Springer Science & Business Media

ISBN: 9781461213802

Category: Mathematics

Page: 426

View: 231

A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.

Author: Kossuth Lajos Tudományegyetem. Matematikai IntézetPublish On: 1993

Szabó WA E. I. Khukhro , Nilpotent Groups and their Automorphisms . ( de
Gruyter Expositions in Mathematics , 8 ) XIII , 252 pages , Walter de Gruyter ,
Berlin – New York , 1993 . In this book linear methods in the theory of nilpotent
groups are ...

Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet

Author: American Mathematical SocietyPublish On: 1993

Evgenii I. Khukhro Marek Jarnicki and Peter Pflug Invariant Distances and
Metrics in Complex Analysis Nilpotent Groups and their Automorphisms 1993. xiv
+ 252 pages . Cloth $ 89.95 ISBN 3-11-013672-4 de Gruyter Expositions in ...

Pronormality , contranormality and generalized nilpotency in infinite groups . ...
20037 Cutolo , Giovanni ( with Nicotera , Chiara ) Subgroups defining automorphisms in locally nilpotent groups . ... ( English summary ) 2004d : 20059
20F24 FC - groups and their generalizations Chernikov , N . S . A note on FC -
groups .

In this review a nilpotent group will always mean a connected and simply
connected Lie group . ... Their unitary representations have a very satisfactory
description and their Plancherel formula is known ; analysis on the quotient of the
group by a ... to a Cauchy principal value , but with the Euclidean distance
replaced by a " gauge ” on Hn which is homogeneous under the automorphisms (
a , c ) → ( t ? a ...

We note now that in spite of the fact that nilpotent non - abelian groups do not
have regular automorphisms of order two , there exist soluble non - abelian groups with regular automorphisms of order two . Example 2 . The infinite
dihedral group ...

Ordered Groups in which Every Automorphism Preserves the Order * V. V.
Bludov Irkutsk State University Irkutsk Russia 1 Introduction We study outer automorphisms of ordered nilpotent groups which preserve the order of G. We
denote the group of all ... Is there a finitely generated ordered nilpotent group G of
class three such that Aut G = Ord G ? * Supported by RFBR , grant 99-01-00335 .
Problem 1.2 .

characteristic nilpotent subgroup C of nilpotency class sc such that the rank of the
quotient group G / C is finite and bounded ... Therefore , in the general 0 € AutG
case , there is a certain reduction to the cases of ( locally case , nilpotent ) torsion
- free groups and periodic groups . ... APPLICATIONS TO ALMOST REGULAR AUTOMORPHISMS Corollary 1 proved useful , for example , in the study of
almost ...

[ 75 ] E . Schenkman , The existence of outer automorphisms of some nilpotent groups of class 2 , Proc . Amer . Math . Soc . ... ( Russian ) [ 79 ] A . I . Mal ' cev ,
Generalized nilpotent algebras and their associated groups , Mat . Sb . ( N . S . )
25 ...

[ 18 ] B . Hartley and G . Shute , Monomorphisms and direct limits of finite groups
of Lie type , Quart . J . Math . Oxford ( 2 ) ... ( 25 ] E . I . Khukhro , “ Nilpotent Groups and their Automorphisms ” , de Gruyter - Verlag , Berlin , 1993 . [ 26 ] E . I .
Khukhro ...

It illustrates that there is no hope to characterize automorphism groups of ULF -
groups , a question raised in [ 47 ] . ... of Zalesskii ' s [ 83 ] in finding certain
torsion - free nilpotent groups of class 2 with prescribed outer automorphism
groups , it ...

Author: Francesco De Giovanni

Publisher: De Gruyter

ISBN: PSU:000025311587

Category: Mathematics

Page: 335

View: 682

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

1 . But the subgroup ( Cp ( QP ! ! ! ) is generated by elements of order < p ” and is
also nilpotent of ( p , k , n ) - bounded class . ... E . I . Khukhro , Nilpotent groups and their automorphisms , de Gruyter , Berlin ( to appear ) . 20 . B . Huppert and N
...

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.

Author: Bertram Huppert

Publisher: Walter de Gruyter

ISBN: 9783110809237

Category: Mathematics

Page: 624

View: 680

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics 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 wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

39 M . N . Ivko , A characterization of groups with a layer - finite periodic part ,
Candidate ( PhD ) dissertation , Inst . Mat . Mekh . Ural . Otdel . ... ( 54 ) E . I .
Khukhro , Nilpotent groups and their automorphisms , de Gruyter , Berlin 1993 . [
55 ] P . G ...

I . ( 1979 ) Fundamentals of the Theory of Groups , Springer - Verlag , New York ,
Berlin ( Translated from Russian : ( 1972 ) , Nauka , Moscow ) . 12 . Khukhro E . I .
( 1993 ) Nilpotent Groups and Their Automorphisms , Walter de Gruyter , Berlin ...

Automorphism. Groups. of. Generalized. McLain. Groups. *. Manfred Droste
Riidiger Gobel Institut fiir Algebra FB 6, ... McLain groups are important for many
questions in group theory, and their construction and properties can be found in
most text ... The field Fp makes G a locally finite p- group and even if Fp is
replaced by a field of characteristic 0, matrix multiplication ensures that G is
locally nilpotent; ...

Author: W.C. Holland

Publisher: Springer Science & Business Media

ISBN: 0792338537

Category: Mathematics

Page: 247

View: 618

The separate areas of Ordered Groups and Infinite Permutation Groups began to converge in significant ways about thirty years ago. Since then, the connection has steadily grown so that now permutation groups are essential to many who work in ordered groups. Ordered groups are of some interest to most of those who work in infinite permutation groups, and there are a number of mathematicians whose main work is exactly in ordered permutation groups, the combination of the two. This book represents the happy confluence of the two subjects, running the spectrum from purely infinite permutation groups through ordered permutation groups to purely ordered groups. Experts in various aspects of these subjects have each contributed a chapter. The articles are surveys of recent and past work in the area and they include extensive bibliographies. Topics include lattice-ordered groups, ordered permutation groups, Jordan groups, reconstruction problems, groups with few orbits, the separation theorem, and automorphisms of symmetric groups. This book is an essential reference for anyone working in ordered groups or infinite permutation groups.