{
  "id": "2011.01176",
  "version": "v1",
  "published": "2020-11-02T18:15:38.000Z",
  "updated": "2020-11-02T18:15:38.000Z",
  "title": "Comparison and Simplicity of Commutator Subgroups of Full Groups",
  "authors": [
    "Hung-Chang Liao"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for a minimal, second countable, locally compact Hausdorff \\'etale groupoid whose unit space is homeomorphic to the Cantor set, if the groupoid has comparison then the commutator subgroup of its full group is simple. This generalizes a result of Bezuglyi and Medynets for Cantor minimal systems and complements Matui's results for topological full groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-02T18:15:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full group",
      "commutator subgroup",
      "comparison",
      "simplicity",
      "locally compact hausdorff etale groupoid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}