{
  "id": "0706.3246",
  "version": "v1",
  "published": "2007-06-22T01:43:58.000Z",
  "updated": "2007-06-22T01:43:58.000Z",
  "title": "On finite groups whose derived subgroup has bounded rank",
  "authors": [
    "Karoly Podoski",
    "Balazs Szegedy"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group with derived subgroup of rank $r$. We prove that $\\gzz\\leq |G'|^{2r}$. Motivated by the results of I. M. Isaacs in \\cite{isa} we show that if $G$ is capable then $\\gz\\leq |G'|^{4r}$. This answers a question of L. Pyber. We prove that if $G$ is a capable $p$-group then the rank of $G/\\mathbf{Z}(G)$ is bounded above in terms of the rank of $G'$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-22T01:43:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D99"
    ],
    "keywords": [
      "finite group",
      "derived subgroup",
      "bounded rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.3246P"
    }
  }
}