{
  "id": "math/0509024",
  "version": "v4",
  "published": "2005-09-01T18:07:32.000Z",
  "updated": "2008-01-08T00:57:53.000Z",
  "title": "Growth and generation in SL_2(Z/pZ)",
  "authors": [
    "H. A. Helfgott"
  ],
  "comment": "21 pages; fourth version - lemmas on escape amended and improved; to appear in Annals of Mathematics",
  "categories": [
    "math.GR",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We show that every subset of SL_2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL_2(Z/pZ), every element of SL_2(Z/pZ) can be expressed as a product of at most O((log p)^c) elements of the union of A and A^{-1}, where c and the implied constant are absolute.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-01-08T00:57:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "20G40",
      "20D60",
      "11B75"
    ],
    "keywords": [
      "generation",
      "group operation",
      "generators",
      "implied constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9024H"
    }
  }
}