{
  "id": "2008.03211",
  "version": "v1",
  "published": "2020-08-07T15:01:18.000Z",
  "updated": "2020-08-07T15:01:18.000Z",
  "title": "On the metabelian property of quotient groups of solvable groups of orientation-preserving homeomorphisms of the line",
  "authors": [
    "Levon Beklaryan"
  ],
  "comment": "6 pages, 1 figure",
  "categories": [
    "math.GR"
  ],
  "abstract": "For the class of solvable groups of homeomorphisms of the line preserving orientation and containing a freely acting element, we establish the metabelianity of the quotient group $G/H_G$, where the elements of the normal subgroup $H_G$ are stabilizers of the minimal set. This fact is an important element in the classification theorem, used, in particular, in the study of the Thompson's group $F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-07T15:01:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E07"
    ],
    "keywords": [
      "quotient group",
      "solvable groups",
      "metabelian property",
      "orientation-preserving homeomorphisms",
      "thompsons group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}