{
  "id": "1002.4853",
  "version": "v5",
  "published": "2010-02-25T19:34:27.000Z",
  "updated": "2012-06-19T18:23:07.000Z",
  "title": "On the Connectivity of the Sylow Graph of a Finite Group",
  "authors": [
    "Francesco G. Russo"
  ],
  "comment": "8 pp. with Appendix; Fundamental revisions have been done",
  "journal": "Advances in Pure Mathematics, Vol. 02, No. 6, 2012, pp.373-378",
  "doi": "10.4236/apm.2012.26058",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The Sylow graph $\\Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $\\mathbf{N}$--closed classes of groups. The connectivity of $\\Gamma(G)$ was proved only few years ago, involving the classification of finite simple groups, and the structure of $G$ may be strongly restricted, once information on $\\Gamma(G)$ are given. The first result of the present paper deals with a condition on $\\mathbf{N}$--closed classes of groups. The second result deals with a computational criterion, related to the connectivity of $\\Gamma(G)$.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-06-19T18:23:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E32",
      "20D20",
      "20F17"
    ],
    "keywords": [
      "finite group",
      "sylow graph",
      "connectivity",
      "closed classes",
      "finite simple groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4853R"
    }
  }
}