{
  "id": "math/0508048",
  "version": "v1",
  "published": "2005-08-01T19:42:16.000Z",
  "updated": "2005-08-01T19:42:16.000Z",
  "title": "On nilpotent groups and conjugacy classes",
  "authors": [
    "Edith Adan-Bante"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a nilpotent group and $a\\in G$. Let $a^G=\\{g^{-1}ag\\mid g\\in G\\}$ be the conjugacy class of $a$ in $G$. Assume that $a^G$ and $b^G$ are conjugacy classes of $G$ with the property that $|a^G|=|b^G|=p$, where $p$ is an odd prime number. Set $a^G b^G=\\{xy\\mid x\\in a^G, y\\in b^G\\}$. Then either $a^G b^G=(ab)^G$ or $a^G b^G$ is the union of at least $\\frac{p+1}{2}$ distinct conjugacy classes. As an application of the previous result, given any nilpotent group $G$ and any conjugacy class $a^G$ of size $p$, we describe the square $a^G a^G$ of $a^G$ in terms of conjugacy classes of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-01T19:42:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotent group",
      "distinct conjugacy classes",
      "odd prime number",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8048A"
    }
  }
}