Groups with Tarski number 5

Abstract

The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. Until now the only numbers which were known to be Tarski numbers of some groups were 4 and 6. We construct a group with Tarski number 5 and mention a related result for Tarski numbers of group actions.

The paper makes substantial use of material from M. Ershov, G. Golan and M. Sapir, The Tarski numbers of groups, http://arxiv.org/abs/1401.2202