arXiv:1702.01631 Abstract | arXiv Analytics

arXiv:1702.01631 [math.DS]Abstract References Reviews Resources

On uniformly recurrent subgroups of finitely generated groups

Published 2017-02-06Version 1

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.

Comments: 8 pages

Categories: math.DS, math.GR

Subjects: 37B05, 20E99

Keywords: finitely generated group, uniformly recurrent subgroup, invariant probability measure, minimal system, finitely generated sofic groups

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