{
  "id": "1112.5530",
  "version": "v2",
  "published": "2011-12-23T08:23:07.000Z",
  "updated": "2012-04-11T11:02:46.000Z",
  "title": "On The Isomorphism Classes Of Transversals III",
  "authors": [
    "Vivek Kumar Jain"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are isomorphic if they are isomorphic with respect to the induced left loop structures. In this paper, we develop a method to calculate the number of isomorphism classes of transversals of $H$ in $G$. Also with the help of this we calculate the number of non-isomorphic left loops of a given order.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-11T11:02:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "20N05"
    ],
    "keywords": [
      "isomorphism classes",
      "left transversal",
      "non-isomorphic left loops",
      "induced left loop structures",
      "binary operation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.5530J"
    }
  }
}