{
  "id": "2306.13363",
  "version": "v1",
  "published": "2023-06-23T08:28:56.000Z",
  "updated": "2023-06-23T08:28:56.000Z",
  "title": "A Characterization of Group Through Isomorphism Classes of Transversals",
  "authors": [
    "Vivek Kumar Jain",
    "Raja Rawat"
  ],
  "comment": "20 pages, 1 table",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on right cosets of H in G is isomorphic to the alternating group on four symbols.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-23T08:28:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "20N05"
    ],
    "keywords": [
      "isomorphism classes",
      "characterization",
      "right cosets",
      "finite index",
      "right transversals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}