{
  "id": "1312.5140",
  "version": "v2",
  "published": "2013-12-18T13:56:26.000Z",
  "updated": "2015-09-02T15:13:18.000Z",
  "title": "Free actions of free groups on countable structures and property (T)",
  "authors": [
    "David M. Evans",
    "Todor Tsankov"
  ],
  "comment": "14 pages. Minor changes to original version",
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "We show that if $G$ is a non-archimedean, Roelcke precompact, Polish group, then $G$ has Kazhdan's property (T). Moreover, if $G$ has a smallest open subgroup of finite index, then $G$ has a finite Kazhdan set. Examples of such $G$ include automorphism groups of countable $\\omega$-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup of $G$ acting freely in all infinite transitive permutation representations of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-18T13:56:26.000Z",
      "comment": "14 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-02T15:13:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A25",
      "20B27",
      "03C15"
    ],
    "keywords": [
      "free groups",
      "free actions",
      "countable structures",
      "smallest open subgroup",
      "infinite permutation groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5140E"
    }
  }
}