Tarski numbers of group actions

Gili Golan

doi:10.4171/GGD/371

Tarski numbers of group actions

Gili Golan

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 language	English
Pages (from-to)	933-950
Number of pages	18
Journal	Groups, Geometry, and Dynamics
Volume	10
Issue number	3
DOIs	https://doi.org/10.4171/GGD/371
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

Amenability
Paradoxical decomposition
Stallings core
Tarski number

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/371

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AB - 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.

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KW - Paradoxical decomposition

KW - Stallings core

KW - Tarski number

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Tarski numbers of group actions

Abstract

Keywords

ASJC Scopus subject areas

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