{
  "id": "1907.10828",
  "version": "v1",
  "published": "2019-07-25T04:00:01.000Z",
  "updated": "2019-07-25T04:00:01.000Z",
  "title": "Short presentations of finite simple groups",
  "authors": [
    "Peter Huxford"
  ],
  "comment": "26 pages, 0 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Guralnick, Kantor, Kassabov and Lubotzky (J. Eur. Math. Soc. 13.2, 2011, 391-458) [GKKL] give 3-generator 7-relator presentations of $A_n$ and $S_n$ with bit-length $O(\\log n)$ for $n\\geq5$. This is the best possible bit-length, since $\\Omega(\\log n)$ bits are required to specify the integer $n$ in the input. However, the generators do not satisfy the relations. This paper considers the relevant arguments given in [GKKL], identifies where the errors occur, and shows how they can be fixed in order to recover this result. The presentations are available in Magma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-25T04:00:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "20D06"
    ],
    "keywords": [
      "finite simple groups",
      "short presentations",
      "bit-length",
      "relevant arguments",
      "errors occur"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}