{
  "id": "1512.08215",
  "version": "v1",
  "published": "2015-12-27T13:13:15.000Z",
  "updated": "2015-12-27T13:13:15.000Z",
  "title": "A characterization of A_5 by its Same-order type",
  "authors": [
    "L. Jafari Taghvasani",
    "M. Zarrin"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a group, de?ne an equivalence relation s as below: 8 g; h 2 G g s h () jgj = jhj the set of sizes of equivalence classes with respect to this relation is called the same-order type of G. Shen et al. (Monatsh. Math. 160 (2010), 337-341.), showed that A5 is the only group with the same-order type f1; 15; 20; 24g. In this paper, among other things, we prove that a nonabelian simple group G has same-order type fr; m; n; kg if and only if G ?= A5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-27T13:13:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "20D06"
    ],
    "keywords": [
      "characterization",
      "same-order type f1",
      "nonabelian simple group",
      "same-order type fr",
      "equivalence relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208215J"
    }
  }
}