{
  "id": "1909.01879",
  "version": "v1",
  "published": "2019-09-04T15:23:57.000Z",
  "updated": "2019-09-04T15:23:57.000Z",
  "title": "Polyhedral products, and relations in the commutator subgroup of a right-angled Coxeter group",
  "authors": [
    "Marina Ilyasova"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "We give a criterion of the existence of a presentation with a single relation for the commutator subgroup $RC_{\\mathscr{K}}'$ of a right-angled Coxeter group $RC_{\\mathscr{K}}$. Namely, we prove that $RC_{\\mathscr{K}}'$ is a one-relator group if and only if $\\mathscr{K}$ is either a $p$-cycle with $p\\geqslant4$ or has the form ($p$-cycle)$*\\Delta^q$ with $p\\geqslant4$ and $g\\geqslant0$, where $\\Delta^q$ is a $q$-simplex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-04T15:23:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "right-angled coxeter group",
      "commutator subgroup",
      "polyhedral products",
      "single relation",
      "one-relator group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}