{
  "id": "2007.06058",
  "version": "v1",
  "published": "2020-07-12T18:25:11.000Z",
  "updated": "2020-07-12T18:25:11.000Z",
  "title": "Half-isomorphisms whose inverses are also half-isomorphisms",
  "authors": [
    "Giliard Souza dos Anjos"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $(G,*)$ and $(G',\\cdot)$ be groupoids. A bijection $f: G \\rightarrow G'$ is called a half-isomorphism if $f(x*y)\\in\\{f(x)\\cdot f(y),f(y)\\cdot f(x)\\}$, for any $ x, y \\in G$. A half-isomorphism of a groupoid onto itself is a half-automorphism. A half-isomorphism $f$ is called special if $f^{-1}$ is also a half-isomorphism. In this paper, necessary and sufficient conditions for the existence of special half-isomorphisms on groupoids and quasigroups are obtained. Furthermore, some examples of non-special half-automorphisms for loops of infinite order are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-12T18:25:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20N02",
      "20N05"
    ],
    "keywords": [
      "sufficient conditions",
      "special half-isomorphisms",
      "non-special half-automorphisms",
      "infinite order",
      "quasigroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}