{
  "id": "1809.07095",
  "version": "v1",
  "published": "2018-09-19T09:32:55.000Z",
  "updated": "2018-09-19T09:32:55.000Z",
  "title": "Some properties of Neumann quasigroups",
  "authors": [
    "Natalia N. Didurik",
    "Victor A. Shcherbacov"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Any Neumann quasigroup $(Q, \\cdot)$ (quasigroup with Neumann identity $ x \\cdot(yz \\cdot yx) = z$ is called Neumann quasigroup) can be presented in the form $x\\cdot y = x-y$, where $(Q, +)$ is an abelian group. Automorphism group of Neumann quasigroup coincides with the group $Aut(Q, +)$. Any Schweizer quasigroup (quasigroup with Schweizer identity $xy \\cdot xz = zy$ is called Schweizer quasigroup) is a Neumann quasigroup and vice versa. Any Neumann quasigroup is a GA-quasigroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-19T09:32:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20N05"
    ],
    "keywords": [
      "properties",
      "schweizer quasigroup",
      "neumann quasigroup coincides",
      "abelian group",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}