{
  "id": "1801.05320",
  "version": "v1",
  "published": "2018-01-16T15:45:43.000Z",
  "updated": "2018-01-16T15:45:43.000Z",
  "title": "Presentations of parabolics in some elementary Chevalley-Demazure groups",
  "authors": [
    "Yuri Santos Rego"
  ],
  "comment": "45 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Given a universal elementary Chevalley-Demazure group $E_\\Phi^{sc}(R)$ for which its (standard) parabolic subgroups are finitely generated, we consider the problem of classifying which parabolics $P(R) \\subset E_\\Phi^{sc}(R)$ are finitely presented. We show that, under mild assumptions, this is equivalent to the finite presentability of a suitable retract of $P$ which contains the Levi factor. If the base ring $R$ is a Dedekind domain of arithmetic type, we combine our results with well-known theorems due to Borel-Serre, Abels, Behr and Bux to give a partial classification of finitely presentable $S$-arithmetic subgroups of parabolics in split reductive linear algebraic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-16T15:45:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "20H25",
      "20G30"
    ],
    "keywords": [
      "presentations",
      "split reductive linear algebraic groups",
      "universal elementary chevalley-demazure group",
      "partial classification",
      "dedekind domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}