Tarski numbers of group actions

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1 Scopus citations


The Tarski number of a group action G O↓ 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 k 4 we construct a faithful transitive action of a free group with Tarski number κ. We also construct a group action G O↓ X with Tarski number 6 such that the Tarski numbers of restrictions of this action to finite index subgroups of G are arbitrarily large.

Original languageEnglish
Pages (from-to)933-950
Number of pages18
JournalGroups, Geometry, and Dynamics
Issue number3
StatePublished - 1 Jan 2016
Externally publishedYes


  • Amenability
  • Paradoxical decomposition
  • Stallings core
  • Tarski number

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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