Combinatorial and Geometric Group Theory, Edinburgh 1993

doi:10.1017/CBO9780511566073

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Edited by Andrew J. Duncan, University of Newcastle upon Tyne, N. D. Gilbert, University of Durham, James Howie, Heriot-Watt University, Edinburgh

Publisher:: Cambridge University Press
Online publication date:: April 2013
Print publication year:: 1994
Online ISBN:: 9780511566073
DOI:: https://doi.org/10.1017/CBO9780511566073

Subjects:: Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Geometry and Topology
Series:: London Mathematical Society Lecture Note Series (204)

58.99 (GBP)

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The ICMS Workshop on Geometric and Combinatorial Methods in Group Theory, held at Heriot-Watt University in 1993, brought together some of the leading research workers in the subject. Some of the survey articles and contributed papers presented at the meeting are collected in this volume. The former cover a number of areas of current interest and include papers by: S. M. Gersten, R. I. Grigorchuk, P. H. Kropholler, A. Lubotzky, A. A. Razborov and E. Zelmanov. The contributed articles, all refereed, range over a wide number of topics in combinatorial and geometric group theory and related topics. The volume represents a summary of the state of knowledge of the field, and as such will be indispensable to all research workers in the area.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Foreword
pp vii-vii
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Participants
pp viii-x
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On bounded languages and the geometry of nilpotent groups
pp 1-15
- By M R Bridson, Princeton University, R H Gilman, Stevens Institute of Technology
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Finitely presented groups and the finite generation of exterior powers
pp 16-28
- By C J B Brookes, Universität Frankfurt
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Semigroup presentations and minimal ideals
pp 29-42
- By C M Campbell, University of St Andrews, E F Robertson, University of St Andrews, N Ruškuc, University of St Andrews, R M Thomas, University of Leicester
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Generalised trees and Λ-trees
pp 43-55
- By I M Chiswell, University of London
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The mathematician who had little wisdom: a story and some mathematics
pp 56-62
- By D E Cohen, Queen Mary and Westfield College
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Palindromic automorphisms of free groups
pp 63-72
- By D J Collins, Queen Mary and Westfield College
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A Freiheitssatz for certain one-relator amalgamated products
pp 73-86
- By B Fine, Fairfield University, F Roehl, University of Alabama, G Rosenberger, Fachbereich Mathematik Universitat
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Isoperimetric functions of groups and exotic cohomology
pp 87-104
- By S M Gersten, University of Utah
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Some embedding theorems and undecidability questions for groups
pp 105-110
- By C McA Gordon, The University of Texas at Austin
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Some results on bounded cohomology
pp 111-163
- By R I Grigorchuk, Moscow Institute of Railway Transportation
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On perfect subgroups of one-relator groups
pp 164-173
- By J Harlander, Universität Frankfurt
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Weight tests and hyperbolic groups
pp 174-183
- By G Huck, Northern Arizona University, S Rosebrock, Institut f. Didaktik der Mathematik
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A non-residually finite, relatively finitely presented group in the variety N2A
pp 184-189
- By O G Kharlampovich, McGill University, M V Sapir, University of Nebraska
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Hierarchical decompositions, generalized Tate cohomology, and groups of type (FP)∞
pp 190-216
- By P H Kropholler, Queen Mary and Westfield College
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Tree-lattices and lattices in Lie groups
pp 217-232
- By A Lubotzky, Hebrew University
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Generalisations of Fibonacci numbers, groups and manifolds
pp 233-238
- By C Maclachlan, University of Aberdeen
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Knotted surfaces in the 4-sphere with no minimal Seifert manifolds
pp 239-246
- By T Maeda, Kansai University
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The higher geometric invariants of modules over Noetherian group rings
pp 247-254
- By H Meinert, Universität Frankfurt
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On calculation of width in free groups
pp 255-258
- By A Yu Ol'shanskii, Moscow State University
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Hilbert modular groups and isoperimetric inequalities
pp 259-268
- By Ch Pittet, Université de Paris-Sud
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On systems of equations in free groups
pp 269-283
- By A A Razborov, Steklov Mathematical Institute
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Cogrowth and essentiality in groups and algebras
pp 284-293
- By A Rosenmann, Universität GH Essen
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Regular geodesic languages for 2-step nilpotent groups
pp 294-299
- By M Stoll, Mathematisches Institut der Universität
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Finding indivisible Nielsen paths for a train track map
pp 300-313
- By E C Turner, SUNYA, Albany
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More on Burnside's problem
pp 314-321
- By E Zelmanov, University of Wisconsin-Madison
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Problem Session
pp 322-325
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Combinatorial and Geometric Group Theory, Edinburgh 1993

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Foreword
pp vii-vii

Participants
pp viii-x

On bounded languages and the geometry of nilpotent groups
pp 1-15

Finitely presented groups and the finite generation of exterior powers
pp 16-28

Semigroup presentations and minimal ideals
pp 29-42

Generalised trees and Λ-trees
pp 43-55

The mathematician who had little wisdom: a story and some mathematics
pp 56-62

Palindromic automorphisms of free groups
pp 63-72

A Freiheitssatz for certain one-relator amalgamated products
pp 73-86

Isoperimetric functions of groups and exotic cohomology
pp 87-104

Some embedding theorems and undecidability questions for groups
pp 105-110

Some results on bounded cohomology
pp 111-163

On perfect subgroups of one-relator groups
pp 164-173

Weight tests and hyperbolic groups
pp 174-183

A non-residually finite, relatively finitely presented group in the variety N2A
pp 184-189

Hierarchical decompositions, generalized Tate cohomology, and groups of type (FP)∞
pp 190-216

Tree-lattices and lattices in Lie groups
pp 217-232

Generalisations of Fibonacci numbers, groups and manifolds
pp 233-238

Knotted surfaces in the 4-sphere with no minimal Seifert manifolds
pp 239-246

The higher geometric invariants of modules over Noetherian group rings
pp 247-254

On calculation of width in free groups
pp 255-258

Hilbert modular groups and isoperimetric inequalities
pp 259-268

On systems of equations in free groups
pp 269-283

Cogrowth and essentiality in groups and algebras
pp 284-293

Regular geodesic languages for 2-step nilpotent groups
pp 294-299

Finding indivisible Nielsen paths for a train track map
pp 300-313

More on Burnside's problem
pp 314-321

Problem Session
pp 322-325

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Combinatorial and Geometric Group Theory, Edinburgh 1993

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