{
  "id": "0912.2368",
  "version": "v2",
  "published": "2009-12-11T22:10:12.000Z",
  "updated": "2011-05-18T18:16:04.000Z",
  "title": "Bounding the residual finiteness of free groups",
  "authors": [
    "Martin Kassabov",
    "Francesco Matucci"
  ],
  "comment": "6 pages, no figures; final version",
  "journal": "Proceedings of the American Mathematical Society 139 (2011), no. 7, 2281-2286",
  "categories": [
    "math.GR"
  ],
  "abstract": "We find a lower bound to the size of finite groups detecting a given word in the free group, more precisely we construct a word w_n of length n in non-abelian free groups with the property that w_n is the identity on all finite quotients of size ~ n^{2/3} or less. This improves on a previous result of Bou-Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-18T18:16:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E05"
    ],
    "keywords": [
      "residual finiteness",
      "lower bound",
      "non-abelian free groups",
      "finite quotients",
      "finite groups detecting"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.2368K"
    }
  }
}