{
  "id": "1604.04415",
  "version": "v1",
  "published": "2016-04-15T09:48:18.000Z",
  "updated": "2016-04-15T09:48:18.000Z",
  "title": "The Grothendieck-Teichmüller group of $PSL(2, q)$",
  "authors": [
    "Pierre Guillot"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "We show that the Grothendieck-Teichm\\\"uller group of $PSL(2, q)$, or more precisely the group $GT_1(PSL(2, q))$ as previously defined by the author, is the product of an elementary abelian 2-group and several copies of the dihedral group of order 8. Moreover, when $q$ is even, we show that it is trivial. We explain how it follows that the moduli field of any \"dessin d'enfant\" whose monodromy group is $PSL(2, q)$ has derived length less than 4. This paper can serve as an introduction to the general results on the Grothendieck-Teichm\\\"uller group of finite groups obtained by the author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-15T09:48:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grothendieck-teichmüller group",
      "general results",
      "monodromy group",
      "elementary abelian",
      "dessin denfant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404415G"
    }
  }
}