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arXiv · 1702.01631

On uniformly recurrent subgroups of finitely generated groups

Gabor Elek
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Abstract

We prove that if $G$ is a finitely generated group and $Z$ is a uniformly recurrent subgroup of $G$ then there exists a minimal system $(X,G)$ with $Z$ as its stability system. This answers a query of Glasner and Weiss \cite{GW} in the case of finitely generated groups. Using the same method (introduced by Alon, Grytczuk, Haluszczak and Riordan \cite{AGHR}) we will prove that finitely generated sofic groups have free Bernoulli-subshifts admitting an invariant probability measure.

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Gabor Elek. 2017-02-06. On uniformly recurrent subgroups of finitely generated groups. https://arxiv.org/abs/1702.01631

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