{
  "id": "1503.04046",
  "version": "v1",
  "published": "2015-03-13T13:04:34.000Z",
  "updated": "2015-03-13T13:04:34.000Z",
  "title": "Finite groups have more conjugacy classes",
  "authors": [
    "Barbara Baumeister",
    "Attila Maróti",
    "Hung P. Tong-Viet"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that for every $\\epsilon > 0$ there exists a $\\delta > 0$ so that every group of order $n \\geq 3$ has at least $\\delta \\log_{2} n/{(\\log_{2} \\log_{2} n)}^{3+\\epsilon}$ conjugacy classes. This sharpens earlier results of Pyber and Keller. Bertram speculates whether it is true that every finite group of order $n$ has more than $\\log_{3}n$ conjugacy classes. We answer Bertram's question in the affirmative for groups with a trivial solvable radical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-13T13:04:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "20D06",
      "20P99"
    ],
    "keywords": [
      "conjugacy classes",
      "finite group",
      "sharpens earlier results",
      "answer bertrams question",
      "bertram speculates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}