{
  "id": "math/0612723",
  "version": "v1",
  "published": "2006-12-22T20:46:20.000Z",
  "updated": "2006-12-22T20:46:20.000Z",
  "title": "Derived Length and Products of Conjugacy Classes",
  "authors": [
    "Edith Adan-Bante"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a supersolvable group and $A$ be a conjugacy class of $G$. Observe that for some integer $\\eta(AA^{-1})>0$, $AA^{-1}=\\{a b^{-1}\\mid a,b\\in A\\}$ is the union of $\\eta(AA^{-1})$ distinct conjugacy classes of $G$. Set ${\\bf C}_G(A)=\\{g\\in G\\mid a^g=a\\text{for all} a\\in A\\}$. Then the derived length of $G/{\\bf C}_G(A)$ is less or equal than $2\\eta(A A^{-1})-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-22T20:46:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived length",
      "distinct conjugacy classes",
      "supersolvable group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12723A"
    }
  }
}