{
  "id": "0807.2027",
  "version": "v3",
  "published": "2008-07-14T19:30:06.000Z",
  "updated": "2009-06-08T15:34:35.000Z",
  "title": "Growth in SL_3(Z/pZ)",
  "authors": [
    "H. A. Helfgott"
  ],
  "comment": "88 pages; Theorem 1.1 is new",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "Let G=SL_3(Z/pZ), p a prime. Let A be a set of generators of G. Then A grows under the group operation. To be precise: denote by |S| the number of elements of a finite set S. Assume |A| < |G|^{1-\\epsilon} for some \\epsilon>0. Then |A\\cdot A\\cdot A|>|A|^{1+\\delta}, where \\delta>0 depends only on \\epsilon. We also study subsets A\\subset G that do not generate G. Other results on growth and generation follow.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-06-08T15:34:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "20G40",
      "20D60",
      "20F65",
      "11B75"
    ],
    "keywords": [
      "group operation",
      "finite set",
      "study subsets",
      "generation",
      "generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 88,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2027H"
    }
  }
}