{
  "id": "0904.2152",
  "version": "v1",
  "published": "2009-04-14T16:13:01.000Z",
  "updated": "2009-04-14T16:13:01.000Z",
  "title": "On conjugacy classes of GL(n,q) and SL(n,q)",
  "authors": [
    "Edith Adan-Bante",
    "John M. Harris"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let GL(n,q) be the group of nxn invertible matrices over a field with q elements, and SL(n,q) be the group of nxn matrices with determinant 1 over a field with q elements. We prove that the product of any two non-central conjugacy classes in GL(n,q) is the union of at least q-1 distinct conjugacy classes, and that the product of any two non-central conjugacy classes in SL(n,q) is the union of at least $\\lceil\\frac{q}{2} \\rceil$ distinct conjugacy classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-14T16:13:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G40",
      "20E45"
    ],
    "keywords": [
      "non-central conjugacy classes",
      "distinct conjugacy classes",
      "nxn matrices",
      "nxn invertible matrices",
      "determinant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2152A"
    }
  }
}