{
  "id": "0804.1396",
  "version": "v1",
  "published": "2008-04-09T02:20:20.000Z",
  "updated": "2008-04-09T02:20:20.000Z",
  "title": "Presentations of finite simple groups: a computational approach",
  "authors": [
    "R. M. Guralnick",
    "W. M. Kantor",
    "M. Kassabov",
    "A. Lubotzky"
  ],
  "comment": "48 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "All nonabelian finite simple groups of rank $n$ over a field of size $q$, with the possible exception of the Ree groups $^2G_2(3^{2e+1})$, have presentations with at most $80 $ relations and bit-length $O(\\log n +\\log q)$. Moreover, $A_n$ and $S_n$ have presentations with 3 generators$,$ 7 relations and bit-length $O(\\log n)$, while $\\SL(n,q)$ has a presentation with 7 generators, $2 5$ relations and bit-length $O(\\log n +\\log q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-09T02:20:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D06",
      "20F05",
      "20J06"
    ],
    "keywords": [
      "computational approach",
      "presentation",
      "nonabelian finite simple groups",
      "bit-length",
      "ree groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1396G"
    }
  }
}