{
  "id": "1805.02090",
  "version": "v1",
  "published": "2018-05-05T18:00:07.000Z",
  "updated": "2018-05-05T18:00:07.000Z",
  "title": "Separability of Schur rings over an abelian group of order 4p",
  "authors": [
    "Grigory Ryabov"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "An $S$-ring (a Schur ring) is said to be separable with respect to a class of groups $\\mathcal{K}$ if every its algebraic isomorphism to an $S$-ring over a group from $\\mathcal{K}$ is induced by a combinatorial isomorphism. We prove that every Schur ring over an abelian group $G$ of order $4p$, where $p$ is a prime, is separable with respect to the class of abelian groups. This implies that the Weisfeiler-Leman dimension of the class of Cayley graphs over $G$ is at most 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-05T18:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "schur ring",
      "order 4p",
      "separability",
      "algebraic isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}