{
  "id": "2003.05356",
  "version": "v1",
  "published": "2020-03-11T15:26:04.000Z",
  "updated": "2020-03-11T15:26:04.000Z",
  "title": "Bounding the number of classes of a finite group in terms of a prime",
  "authors": [
    "Attila Maróti",
    "Iulian I. Simion"
  ],
  "comment": "To appear in Journal of Group Theory",
  "doi": "10.1515/jgth-2019-0144",
  "categories": [
    "math.GR"
  ],
  "abstract": "H\\'ethelyi and K\\\"ulshammer showed that the number of conjugacy classes $k(G)$ of any solvable finite group $G$ whose order is divisible by the square of a prime $p$ is at least $(49p+1)/60$. Here an asymptotic generalization of this result is established. It is proved that there exists a constant $c>0$ such that for any finite group $G$ whose order is divisible by the square of a prime $p$ we have $k(G) \\geq cp$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-11T15:26:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy classes",
      "asymptotic generalization",
      "solvable finite group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}