{
  "id": "2403.16769",
  "version": "v2",
  "published": "2024-03-25T13:46:18.000Z",
  "updated": "2024-06-13T03:54:36.000Z",
  "title": "Dynamics of primitive elements under group actions",
  "authors": [
    "Pratyush Mishra"
  ],
  "comment": "Added section 9 and a few minor corrections have been made",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "We investigate group actions in which certain primitive elements fix a point, while not all group elements possess this property when acting upon some space. Using similar dynamical tools, we introduce the notion of Nielsen girth and prove the existence of groups with infinite girth but having finite Nielsen girth.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-13T03:54:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S25",
      "37E05",
      "20-08"
    ],
    "keywords": [
      "group actions",
      "finite nielsen girth",
      "group elements possess",
      "similar dynamical tools",
      "primitive elements fix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}