{
  "id": "0810.5494",
  "version": "v1",
  "published": "2008-10-30T14:15:54.000Z",
  "updated": "2008-10-30T14:15:54.000Z",
  "title": "A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite group",
  "authors": [
    "Colin Reid"
  ],
  "comment": "25 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper, we consider Problem 14.44 in the Kourovka notebook, which is a conjecture about the number of conjugacy classes of a finite group. While elementary, this conjecture is still open and appears to elude any straightforward proof, even in the soluble case. However, we do prove that a minimal soluble counterexample must have certain properties, in particular that it must have Fitting height at least 3 and order at least 2000.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-30T14:15:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy classes",
      "kourovka notebook concerning",
      "finite group",
      "conjecture",
      "minimal soluble counterexample"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.5494R"
    }
  }
}