Groups St Andrews 2005. Volume 1 / edited by C. M. Campbell [and three others].

Format:

Book

Contributor:

Campbell, C. M., 1942- editor.

Series:

London Mathematical Society lecture note series ; 339.

London Mathematical Society lecture note series ; 339

Language:

English

Subjects (All):

Group theory--Congresses.

Group theory.

Physical Description:

1 online resource (x, 355 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Language Note:

English

Summary:

'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A&M, USA). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

Contents:

Cover; Title; Copyright; Contents of Volume 1; Contents of Volume 2; Introduction; Aspects of Infinite Permutation Groups; Abstract; 1 Notation and terminology; 2 The random graph; 2.1 B-groups; 2.2 The Erdős-Rényi Theorem; 2.3 Properties of R; 2.4 Properties of Aut(R); 2.5 Topology; 2.6 Reducts of R; 3 Homogeneous relational structures; 3.1 Fraïssé's Theorem; 3.2 Applications; 3.3 Homogeneous structures; 3.4 Some recent connections; 4 Oligomorphic permutation groups; 4.1 Definition and basic properties; 4.2 General properties; 4.3 Highly set-transitive groups; 4.4 Direct and wreath products

4.5 Growth rates4.6 Graded algebras; 5 The Urysohn space; 6 Further topics; 6.1 Finitary permutation groups; 6.2 Jordan groups; 6.3 Maximal subgroups of Sym(Ω); References; Self-Similarity and Branching in Group Theory; Introduction; 1 Self-similar objects; 2 Actions on rooted trees; 3 Self-similar groups; 3.1 General definition; 3.2 Automaton groups; 3.3 Problems; 4 Iterated monodromy groups; 5 Branch groups; 5.1 Geometric definition of a branch group; 5.2 Algebraic definition of a branch group; 5.3 Just infinite branch groups; 5.4 Minimality; 5.5 Problems; 6 Growth of groups

6.1 Word growth6.2 Uniformly exponential growth; 6.3 Torsion growth; 6.4 Subgroup growth; 6.5 Problems; 7 Amenability; 7.1 Definition; 7.2 Elementary classes; 7.3 Tarski numbers; 7.4 Other topics related to amenability; 7.5 Problems; 8 Schreier graphs related to self-similar groups; 8.1 Contracting actions and limit spaces; 8.2 Cayley and Schreier spectra; 8.3 Problems; Acknowledgments; References; On Surface Groups: Motivating Examples in Combinatorial Group Theory; Abstract; 1 Introduction; 2 Subgroup Structure and the Freiheitssatz; 3 The n-Free Property; 4 The Extension Property

5 The Elementary Free Property and the Tarski Problem6 Tame Automorphisms and the Surface Group Conjecture; 7 Small Cancellation Theory; 8 Test Words and Generic Elements; 9 Algebraic Generalizations of Discrete Groups; References; Nilpotent p-Algebras and Factorized p-Groups; Abstract; 1 Introduction; 2 Some open problems; 3 The adjoint group of a finite nilpotent algebra; 4 The nilpotency class of a nilpotent algebra and connections with finite p-groups; 5 Hilbert functions of commutative nilpotent algebras; 6 Products of finite p-groups and their ranks; 7 On Eggert's conjecture; References

Classification of Finite Groups by the Number of Element CentralizersAbstract; 1 Introduction; 2 Distinct Centralizers of some Finite Groups; 3 On Primitive 6- and 7-Centralizers Groups; References; Algorithmic use of the Mal'cev Correspondence; Abstract; 1 Introduction; 2 Mal'cev correspondence; 3 Polycyclic presentations; 4 Algorithmic realization of the Mal'cev correspondence; 5 Collection in polycyclic groups; 6 Runtimes; References; Minimal but Inefficient Presentations for Semi-Direct Products of Finite Cyclic Monoids; Abstract; 1 Introduction

2 The p-Cockcroft property for the semi-direct products of finite cyclic monoids

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88265-1

1-107-36783-2

1-107-37237-2

1-107-36292-X

1-107-36861-8

1-299-40543-6

1-107-36537-6

0-511-72121-8

OCLC:

843203442