{
  "id": "1309.0989",
  "version": "v1",
  "published": "2013-09-03T06:58:51.000Z",
  "updated": "2013-09-03T06:58:51.000Z",
  "title": "On schurity of finite abelian groups",
  "authors": [
    "Sergei Evdokimov",
    "István Kovács",
    "Ilya Ponomarenko"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "A finite group $G$ is called a Schur group, if any Schur ring over $G$ is associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this paper it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any non-cyclic abelian Schur group of odd order is isomorphic to $Z_3\\times Z_{3^k}$ or $Z_3\\times Z_3\\times Z_p$ where $k\\ge 1$ and $p$ is a prime. In addition, we prove that $Z_2\\times Z_2\\times Z_p$ is a Schur group for every prime $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-03T06:58:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "20B25"
    ],
    "keywords": [
      "finite abelian groups",
      "non-cyclic abelian schur group",
      "abelian schur group belongs",
      "cyclic schur groups",
      "right translations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0989E"
    }
  }
}