{
  "id": "math/0504156",
  "version": "v1",
  "published": "2005-04-07T19:36:31.000Z",
  "updated": "2005-04-07T19:36:31.000Z",
  "title": "Conjugacy classes and finite $p$-groups",
  "authors": [
    "Edith Adan-Bante"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite $p$-group, where $p$ is a prime number, and $a\\in G$. Denote by $\\Cl(a)=\\{gag^{-1}\\mid g\\in G\\}$ the conjugacy class of $a$ in $G$. Assume that $|\\Cl(a)|=p^n$. Then $\\Cl(a)\\Cl(a^{-1})=\\{xy\\mid x\\in \\Cl(a), y\\in \\Cl(a^{-1})\\}$ is the union of at least $n(p-1)+1$ distinct conjugacy classes of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-07T19:36:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distinct conjugacy classes",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4156A"
    }
  }
}