Tarski numbers of group actions

  • Gili Golan

    Bar-Ilan University, Ramat Gan, Israel

Abstract

The Tarski number of a group action GXG \curvearrowright X is the minimal number of pieces in a paradoxical decomposition of it. In this paper we solve the problem of describing the set of Tarski numbers of group actions. Namely, for any k4k \ge 4 we construct a faithful transitive action of a free group with Tarski number kk. We also construct a group action GXG \curvearrowright X with Tarski number 66 such that the Tarski numbers of restrictions of this action to finite index subgroups of GG are arbitrarily large.

Cite this article

Gili Golan, Tarski numbers of group actions. Groups Geom. Dyn. 10 (2016), no. 3, pp. 933–950

DOI 10.4171/GGD/371