English

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 XX is locally finite if and only if XX 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