Twisted Brin-Thompson groups
Abstract
We construct a family of infinite simple groups that we call twisted Brin-Thompson groups, generalizing Brin's higher-dimensional Thompson groups sV (s∈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 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 Fn-1 but not of type Fn, for arbitrary n∈N. This provides the second known infinite family of simple groups distinguished by their finiteness properties.
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