{
  "id": "1205.0643",
  "version": "v1",
  "published": "2012-05-03T08:14:01.000Z",
  "updated": "2012-05-03T08:14:01.000Z",
  "title": "On solubility of groups with finitely many centralizers",
  "authors": [
    "Mohammad Zarrin"
  ],
  "comment": "to appear in Bulletin of the Iranian Mathematical Society",
  "categories": [
    "math.GR"
  ],
  "abstract": "For any group G, let C(G) denote the set of centralizers of G. We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n. In this note, we prove that every finite Cn-group with n ? 21 is soluble and this estimate is sharp. Moreover, we prove that every finite Cn-group with |G| < 30n+15 19 is non-nilpotent soluble. This result gives a partial answer to a conjecture raised by A. Ashrafi in 2000.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-03T08:14:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "centralizers",
      "finite cn-group",
      "solubility",
      "partial answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0643Z"
    }
  }
}