{
  "id": "1607.06456",
  "version": "v1",
  "published": "2016-07-21T18:18:43.000Z",
  "updated": "2016-07-21T18:18:43.000Z",
  "title": "Bounds on the number of conjugacy classes of the symmetric and alternating groups",
  "authors": [
    "Bret Benesh",
    "Cong Tuan Son Van"
  ],
  "comment": "3 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group with Sylow subgroups $P_1,\\ldots,P_n$, and let $k(G)$ denote the number of conjugacy classes of $G$. Pyber asked if $k(G) \\leq \\prod_{i=1}^n k(P_i)$ for all finite groups $G$. With the help of GAP, we prove that Pyber's inequality holds for all symmetric and alternating groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-21T18:18:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B30",
      "20E45"
    ],
    "keywords": [
      "conjugacy classes",
      "alternating groups",
      "finite group",
      "pybers inequality holds",
      "sylow subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}