{
  "id": "math/0502221",
  "version": "v1",
  "published": "2005-02-11T05:43:57.000Z",
  "updated": "2005-02-11T05:43:57.000Z",
  "title": "Diameters of Cayley graphs of SL_n(Z/kZ)",
  "authors": [
    "M. Kassabov",
    "T. R. Riley"
  ],
  "comment": "11 pages, no figures",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SL_n(Z/kZ) associated to a standard two-element generating set, is at most a constant times n^2 ln k. This answers a question of A. Lubotzky concerning SL_n(F_p) and is unexpected because these Cayley graphs do not form an expander family. Our proof amounts to a quick algorithm for finding short words representing elements of SL_n(Z/kZ).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-11T05:43:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "05C25",
      "05C35",
      "20D06"
    ],
    "keywords": [
      "cayley graph",
      "standard two-element generating set",
      "finding short words representing elements",
      "constant times",
      "quick algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2221K"
    }
  }
}