{
  "id": "2403.14779",
  "version": "v1",
  "published": "2024-03-21T18:50:30.000Z",
  "updated": "2024-03-21T18:50:30.000Z",
  "title": "Free products of bi-orderable groups",
  "authors": [
    "Kyrylo Muliarchyk"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering. Our method relies on the dynamical realization of bi-ordered groups. We also show that the natural action of the automorphism group $Aut(F_2)$ on $F_2$ does not have dense orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-21T18:50:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05F15",
      "20F60"
    ],
    "keywords": [
      "free product",
      "bi-orderable groups",
      "bi-ordered groups",
      "left-order groups",
      "method relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}