{
  "id": "1511.02374",
  "version": "v1",
  "published": "2015-11-07T16:42:57.000Z",
  "updated": "2015-11-07T16:42:57.000Z",
  "title": "On Schur p-groups of odd order",
  "authors": [
    "Grigory Ryabov"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "A finite group $G$ is called a Schur group if any $S$-ring over $G$ is associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. We prove that the groups $\\mathbb{Z}_3\\times \\mathbb{Z}_{3^n}$, where $n\\geq 1$, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur $p$-group, where $p$ is an odd prime, is isomorphic to $\\mathbb{Z}_3\\times \\mathbb{Z}_3 \\times \\mathbb{Z}_3$ or $\\mathbb{Z}_3\\times \\mathbb{Z}_{3^n}$, $n\\geq 1$ .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-07T16:42:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "20B30"
    ],
    "keywords": [
      "odd order",
      "schur p-groups",
      "schur group",
      "natural way",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102374R"
    }
  }
}