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arXiv · 1406.5689

Tarski numbers of group actions

Gili Golan
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Abstract

The Tarski number of an action of a group G on a set X is the minimal number of pieces in a paradoxical decomposition of it. For any k>3 we construct a faithful transitive action of a free group of rank k-1 with Tarski number k. Using similar techniques we construct a group action of a free group F with Tarski number 6 such that the Tarski numbers of restrictions of this action to finite index subgroups of F are arbitrarily large.

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Gili Golan. 2014-06-22. Tarski numbers of group actions. https://arxiv.org/abs/1406.5689

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