On uniformly recurrent subgroups of finitely generated groups

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.

8 pages

References in corpus (1)

• Uniformly recurrent subgroups and the ideal structure of reduced crossed products

Cited by in corpus (2)

• Free Subshifts with Invariant Measures from the Lovász Local Lemma
• On minimal actions of countable groups