{
  "id": "1701.08853",
  "version": "v1",
  "published": "2017-01-30T22:12:55.000Z",
  "updated": "2017-01-30T22:12:55.000Z",
  "title": "Elementary equivalence vs commensurability for hyperbolic groups",
  "authors": [
    "Vincent Guirardel",
    "Gilbert Levitt",
    "Rizos Sklinos"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "We study to what extent torsion-free (Gromov)-hyperbolic groups are elementarily equivalent to their finite index subgroups. In particular, we prove that a hyperbolic limit group either is a free product of cyclic groups and surface groups, or admits infinitely many subgroups of finite index which are pairwise non elementarily equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-30T22:12:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F70",
      "20F67"
    ],
    "keywords": [
      "hyperbolic groups",
      "elementary equivalence",
      "commensurability",
      "finite index subgroups",
      "hyperbolic limit group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}