{
  "id": "1603.06804",
  "version": "v1",
  "published": "2016-03-22T14:22:09.000Z",
  "updated": "2016-03-22T14:22:09.000Z",
  "title": "Subgroup graph methods for presentations of finitely generated groups and the connectivity of associated simplicial complexes",
  "authors": [
    "Cora Welsch"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this article we generalize the theory of subgroup graphs of subgroups of free groups to finite index subgroups $H$ of finitely generated groups $G$. We study and prove various properties of $H$ in relation to its subgroup graph $\\Gamma(H)$. For a finitely generated group $G$ we consider the poset $P_{\\text{fi}}(G)$ of all right cosets of all proper finite index subgroups of $G$. We use the theory of subgroup graphs to prove that for many finitely generated infinite groups the order complex $\\Delta P_{\\text{fi}} (G)$ and the corresponding nerve complex are contractible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-22T14:22:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finitely generated group",
      "subgroup graph methods",
      "associated simplicial complexes",
      "presentations",
      "connectivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}