{
  "id": "0905.1342",
  "version": "v2",
  "published": "2009-05-08T21:24:39.000Z",
  "updated": "2009-07-07T16:03:03.000Z",
  "title": "On conjugacy classes and derived length",
  "authors": [
    "Edith Adan-Bante"
  ],
  "comment": "5 pages. Correction of typos and other misfortunes",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and $A$, $B$ and $D$ be conjugacy classes of $ G$ with $D\\subseteq AB=\\{xy\\mid x\\in A, y\\in B\\}$. Denote by $\\eta(AB)$ the number of distinct conjugacy classes such that $AB$ is the union of those. Set ${\\bf C}_G(A)=\\{g\\in G\\mid x^g=x {for all} x\\in A\\}$. If $AB=D$ then ${\\bf C}_G(D)/({\\bf C}_G(A)\\cap{\\bf C}_G(B))$ is an abelian group. If, in addition, $G$ is supersolvable, then the derived length of ${\\bf C}_G(D)/({\\bf C}_G(A)\\cap{\\bf C}_G(B))$ is bounded above by $2\\eta(AB)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-07T16:03:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived length",
      "distinct conjugacy classes",
      "abelian group",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1342A"
    }
  }
}