{
  "id": "2401.03335",
  "version": "v1",
  "published": "2023-11-14T06:26:26.000Z",
  "updated": "2023-11-14T06:26:26.000Z",
  "title": "A remark on normal closures in free products of groups",
  "authors": [
    "Dali Zangurashvili"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It is shown that a nontrivial normal subgroup $N$ of a group $G$ is a free factor of the $N$'s normal closure in the $G$'s free product with arbitrary nontrivial groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-14T06:26:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20E07",
      "20E15",
      "20J15"
    ],
    "keywords": [
      "normal closure",
      "free product",
      "nontrivial normal subgroup",
      "arbitrary nontrivial groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}