{
  "id": "2104.12994",
  "version": "v1",
  "published": "2021-04-27T05:58:15.000Z",
  "updated": "2021-04-27T05:58:15.000Z",
  "title": "Gyrogroups associated with groups",
  "authors": [
    "Ratan Lal",
    "Vipul Kakkar"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper, we study the properties of the associated gyrogroup ${^\\circ}G$ of a given group $G$ of nilpotency class $3$. We have proved that if $3$ does not divide the order of the group $G$, then the nilpotency class of the associated gyrogroup ${^\\circ}G$ is same as that of the group $G$. We have also studied the problem of abelian inner mapping group in this context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T05:58:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotency class",
      "associated gyrogroup",
      "abelian inner mapping group",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}