{
  "id": "1702.01631",
  "version": "v1",
  "published": "2017-02-06T14:41:42.000Z",
  "updated": "2017-02-06T14:41:42.000Z",
  "title": "On uniformly recurrent subgroups of finitely generated groups",
  "authors": [
    "Gabor Elek"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-06T14:41:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "20E99"
    ],
    "keywords": [
      "finitely generated group",
      "uniformly recurrent subgroup",
      "invariant probability measure",
      "minimal system",
      "finitely generated sofic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}