{
  "id": "1005.0015",
  "version": "v2",
  "published": "2010-04-30T20:37:54.000Z",
  "updated": "2011-12-09T19:08:27.000Z",
  "title": "Alternating quotients of free groups",
  "authors": [
    "Henry Wilton"
  ],
  "comment": "11 pages, 5 figures. Referee's comments incorporated. To appear in L'Enseignement Math\\'ematique",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We strengthen Marshall Hall's Theorem to show that free groups are locally extended residually alternating. Let F be any free group of rank at least two, let H be a finitely generated subgroup of infinite index in F and let {g_1,...,g_n} be a finite subset of F-H. Then there is a surjection f from F to a finite alternating group such that f(g_i) is not in f(H) for any i. The techniques of this paper can also provide symmetric quotients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-09T19:08:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "20E26"
    ],
    "keywords": [
      "free group",
      "alternating quotients",
      "strengthen marshall halls theorem",
      "infinite index",
      "symmetric quotients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.0015W"
    }
  }
}