Characterizations of locally finite actions of groups on sets
Group Theory
2020-11-09 v3 Operator Algebras
Abstract
We show that an action of a group on a set is locally finite if and only if is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite.
Keywords
Cite
@article{arxiv.1606.08262,
title = {Characterizations of locally finite actions of groups on sets},
author = {Eduardo Scarparo},
journal= {arXiv preprint arXiv:1606.08262},
year = {2020}
}
Comments
4 pages. Minor clarification made in the paragraph after Remark 2.6. To appear in the Glasgow Mathematical Journal