Volume 26, issue 3 (2022)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Twisted Brin–Thompson groups

James Belk and Matthew C B Zaremsky

Geometry & Topology 26 (2022) 1189–1223
Abstract

We construct a family of infinite simple groups that we call twisted Brin–Thompson groups, generalizing Brin’s higher-dimensional Thompson groups sV for s . We use twisted Brin–Thompson groups to prove a variety of results regarding simple groups. For example, we prove that every finitely generated group embeds quasi-isometrically as a subgroup of a two-generated simple group, strengthening a result of Bridson. We also produce examples of simple groups that contain every sV and hence every right-angled Artin group, including examples of type  F and a family of examples of type F n1 but not of type  F n for arbitrary n . This provides the second known infinite family of simple groups distinguished by their finiteness properties.

Keywords
Thompson group, finiteness properties, simple group, right-angled Artin group, quasi-isometry, oligomorphic, Cantor space
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20E32, 57M07
References
Publication
Received: 13 February 2020
Accepted: 1 May 2021
Published: 3 August 2022
Proposed: Martin R Bridson
Seconded: Mladen Bestvina, David M Fisher
Authors
James Belk
School of Mathematics and Statistics
University of St Andrews
St Andrews
United Kingdom
Matthew C B Zaremsky
Department of Mathematics and Statistics
University at Albany (SUNY)
Albany, NY
United States