{
  "id": "1910.04230",
  "version": "v1",
  "published": "2019-10-09T20:05:57.000Z",
  "updated": "2019-10-09T20:05:57.000Z",
  "title": "Morphisms between right-angled Coxeter groups: the two-dimensional case",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "35 pages, 3 figures. Comments are welcome!",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "In this article, given two finite simplicial graphs $\\Gamma_1$ and $\\Gamma_2$ where $\\Gamma_2$ is triangle-free, we state and prove a complete description of the possible morphisms $C(\\Gamma_1) \\to C(\\Gamma_2)$ between the right-angled Coxeter groups $C(\\Gamma_1)$ and $C(\\Gamma_2)$. As an application, we show that, if $C(\\Gamma_1)$ is isomorphic to a subgroup of $C(\\Gamma_2)$, then the ball of radius $8|\\Gamma_1||\\Gamma_2|$ in $C(\\Gamma_2)$ contains the basis of a subgroup isomorphic to $C(\\Gamma_1)$. This provides an algorithm determining whether or not, among two given two-dimensional right-angled Coxeter groups, one is isomorphic to a subgroup of the other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-09T20:05:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20F55",
      "20F10"
    ],
    "keywords": [
      "two-dimensional case",
      "two-dimensional right-angled coxeter groups",
      "finite simplicial graphs",
      "complete description",
      "subgroup isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}