{
  "id": "1708.03245",
  "version": "v1",
  "published": "2017-08-10T14:57:18.000Z",
  "updated": "2017-08-10T14:57:18.000Z",
  "title": "Finite $p$-Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes",
  "authors": [
    "Tushar Kanta Naik",
    "Rahul Dattatraya Kitture",
    "Manoj K. Yadav"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It is proved that, for a prime $p>2$ and integer $n\\geq 1$, finite $p$-groups of nilpotency class $3$ and having only two conjugacy class sizes $1$ and $p^n$ exist if and only if $n$ is even; moreover, for a given even positive integer, such a group is unique up to isoclinism (in the sense of Philip Hall).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-10T14:57:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20E45"
    ],
    "keywords": [
      "conjugacy class sizes",
      "nilpotency class",
      "philip hall",
      "isoclinism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}