{
  "id": "1301.3638",
  "version": "v1",
  "published": "2013-01-16T10:02:36.000Z",
  "updated": "2013-01-16T10:02:36.000Z",
  "title": "A finiteness condition on the coefficients of the probabilistic zeta function",
  "authors": [
    "Duong Hoang Dung",
    "Andrea Lucchini"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We discuss whether finiteness properties of a profinite group $G$ can be deduced from the coefficients of the probabilistic zeta function $P_G(s)$. In particular we prove that if $P_G(s)$ is rational and all but finitely many non abelian composition factors of $G$ are isomorphic to $PSL(2,p)$ for some prime $p$, then $G$ contains only finitely many maximal subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-16T10:02:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20D06",
      "20P05",
      "11M41"
    ],
    "keywords": [
      "probabilistic zeta function",
      "finiteness condition",
      "coefficients",
      "non abelian composition factors",
      "profinite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3638H"
    }
  }
}