{
  "id": "1504.00273",
  "version": "v1",
  "published": "2015-04-01T15:52:21.000Z",
  "updated": "2015-04-01T15:52:21.000Z",
  "title": "On Alternating and Symmetric Groups Which Are Quasi OD-Characterizabile",
  "authors": [
    "Ali Reza Moghaddamfar"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\Gamma(G)$ be the prime graph associated with a finite group $G$ and $D(G)$ be the degree pattern of $G$. A finite group $G$ is said to be $k$-fold OD-characterizable if there exist exactly $k$ non-isomorphic groups $H$ such that $|H|=|G|$ and $D(H)=D(G)$. The purpose of this article is twofold. First, it shows that the symmetric group $S_{27}$ is $38$-fold OD-charaterizable. Second, it shows that there exist many infinite families of alternating and symmetric groups, $\\{A_n\\}$ and $\\{S_n\\}$, which are $k$-fold OD-characterizable with $k>3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-01T15:52:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric group",
      "quasi od-characterizabile",
      "finite group",
      "alternating",
      "fold od-characterizable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150400273M"
    }
  }
}