Twisted Brin-Thompson groups

Belk, J. and Zaremsky, M. C. B. (2022) Twisted Brin-Thompson groups. Geometry and Topology, 26(3), pp. 1189-1223. (doi: 10.2140/gt.2022.26.1189)

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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 2 N. 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 quasiisometrically 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 F1 and a family of examples of type Fn1 but not of type Fn for arbitrary n 2 N. This provides the second known infinite family of simple groups distinguished by their finiteness properties.

Item Type:Articles
Additional Information:ks. During the creation of this paper, Belk was partially supported by EPSRC grant EP/R032866/1 and Zaremsky was partially supported by grant #635763 from the Simons Foundat
Glasgow Author(s) Enlighten ID:Belk, Dr Jim
Authors: Belk, J., and Zaremsky, M. C. B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geometry and Topology
Publisher:Mathematical Sciences Publishers
ISSN (Online):1364-0380
Published Online:03 August 2022
Copyright Holders:Copyright © 2022 Mathematical Sciences Publishers
First Published:First published in Geometry and Topology 26(3): 1189-1223
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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