Groups: Topological, Combinatorial and Arithmetic Aspects

doi:10.1017/CBO9780511550706

In 1999 a number of eminent mathematicians were invited to Bielefeld to present lectures at a conference on topological, combinatorial and arithmetic aspects of (infinite) groups. The present volume consists of survey and research articles invited from participants in this conference. Topics covered include topological finiteness properties of groups, Kac-Moody groups, the theory of Euler characteristics, the connection between groups, formal languages and automata, the Magnus-Nielsen method for one-relator groups, atomic and just infinite groups, topology in permutation groups, probabilistic group theory, the theory of subgroup growth, hyperbolic lattices in dimension three, generalised triangle groups and reduction theory. All contributions are written in a relaxed and attractive style, accessible not only to specialists, but also to good graduate and post-graduate students, who will find inspiration for a number of basic research projects at various levels of technical difficulty.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Contents

Frontmatter
pp i-iv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Contents
pp v-vi
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

List of authors and participants
pp vii-x
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Preface
pp xi-xvi
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

1 - Reductive groups as metric spaces
pp 1-20
- By H. Abels
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

2 - Finiteness properties of groups acting on twin buildings
pp 21-26
- By P. Abramenko
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

3 - Higher finiteness properties of S-arithmetic groups in the function field case I
pp 27-42
- By H. Behr
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

4 - Controlled topology and group actions
pp 43-63
- By R. Bieri, R. Geoghegan
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

5 - Finiteness properties of soluble S-arithmetic groups – A survey
pp 64-92
- By K.-U. Bux
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

6 - Topology in permutation groups
pp 93-105
- By P. J. Cameron
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

7 - Euler characteristics of discrete groups
pp 106-254
- By I. M. Chiswell
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

8 - Intersections of Magnus subgroups of one-relator groups
pp 255-296
- By D. J. Collins
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

9 - A minimality property of certain branch groups
pp 297-305
- By R. I. Grigorchuk, J. S. Wilson
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

10 - Lattices with non-integral character
pp 306-317
- By H. Helling
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

11 - Some applications of probability in group theory
pp 318-326
- By Avinoam Mann
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

12 - Parity patterns in Hecke groups and Fermat primes
pp 327-374
- By T. W. Müller, For Wilfried Imrich on the occasion of his sixtieth birthday
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

13 - Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms
pp 375-404
- By V. Nekrashevych, S. Sidki
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

14 - The mapping class group of the twice punctured torus
pp 405-486
- By J. R. Parker, C. Series
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

15 - Kac–Moody groups: split and relative theories. Lattices
pp 487-541
- By B. Remy
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

16 - On the finite images of infinite groups
pp 542-563
- By D. Segal
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

17 - Pseudo-finite generalized triangle groups
pp 564-587
- By E. B. Vinberg, R. Kaplinsky
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Metrics

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Groups

Topological, Combinatorial and Arithmetic Aspects

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-iv

Contents
pp v-vi

List of authors and participants
pp vii-x

Preface
pp xi-xvi

1 - Reductive groups as metric spaces
pp 1-20

2 - Finiteness properties of groups acting on twin buildings
pp 21-26

3 - Higher finiteness properties of S-arithmetic groups in the function field case I
pp 27-42

4 - Controlled topology and group actions
pp 43-63

5 - Finiteness properties of soluble S-arithmetic groups – A survey
pp 64-92

6 - Topology in permutation groups
pp 93-105

7 - Euler characteristics of discrete groups
pp 106-254

8 - Intersections of Magnus subgroups of one-relator groups
pp 255-296

9 - A minimality property of certain branch groups
pp 297-305

10 - Lattices with non-integral character
pp 306-317

11 - Some applications of probability in group theory
pp 318-326

12 - Parity patterns in Hecke groups and Fermat primes
pp 327-374

13 - Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms
pp 375-404

14 - The mapping class group of the twice punctured torus
pp 405-486

15 - Kac–Moody groups: split and relative theories. Lattices
pp 487-541

16 - On the finite images of infinite groups
pp 542-563

17 - Pseudo-finite generalized triangle groups
pp 564-587

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

Groups

Topological, Combinatorial and Arithmetic Aspects

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information