{
  "id": "1110.3286",
  "version": "v1",
  "published": "2011-10-14T18:27:40.000Z",
  "updated": "2011-10-14T18:27:40.000Z",
  "title": "Quantifying the Residual Properties of Gamma-Limit Groups",
  "authors": [
    "Brent B. Solie"
  ],
  "comment": "22 pages, 6 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let Gamma be a fixed hyperbolic group. The Gamma-limit groups of Sela are exactly the finitely generated, fully residually Gamma groups. We give a new invariant of Gamma-limit groups called Gamma-discriminating complexity and show that the Gamma-discriminating complexity of any Gamma-limit group is asymptotically dominated by a polynomial. Our proof relies on an embedding theorem of Kharlampovich-Myasnikov which states that a Gamma-limit group embeds in an iterated extension of centralizers over Gamma. The result then follows from our proof that if G is an iterated extension of centralizers over Gamma, the G-discriminating complexity of a rank n extension of a cyclic centralizer of G is asymptotically dominated by a polynomial of degree n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-14T18:27:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "residual properties",
      "gamma-limit group embeds",
      "iterated extension",
      "gamma-discriminating complexity",
      "fully residually gamma groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3286S"
    }
  }
}