On uniformly recurrent subgroups of finitely generated groups

2017/02/06 by Elek, Gabor
#20E99 #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1702.01631

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 \citeGW in the case of finitely generated groups. Using the same method (introduced by Alon, Grytczuk, Haluszczak and Riordan \citeAGHR) we will prove that finitely generated sofic groups have free Bernoulli-subshifts admitting an invariant probability measure.

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