{
  "id": "2007.14696",
  "version": "v1",
  "published": "2020-07-29T09:24:46.000Z",
  "updated": "2020-07-29T09:24:46.000Z",
  "title": "On 2-closures of rank 3 groups",
  "authors": [
    "Saveliy V. Skresanov"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "A permutation group $G$ on $\\Omega$ is called a rank 3 group if it has precisely three orbits in its induced action on $\\Omega \\times \\Omega$. The largest permutation group on $\\Omega$ having the same orbits as $G$ on $\\Omega \\times \\Omega$ is called the 2-closure of $G$. A description of 2-closures of rank 3 groups is given. As a special case, it is proved that 2-closure of a primitive one-dimensional affine rank 3 permutation group of sufficiently large degree is also affine and one-dimensional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-29T09:24:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "20B15",
      "05E18"
    ],
    "keywords": [
      "largest permutation group",
      "primitive one-dimensional affine rank",
      "special case",
      "sufficiently large degree",
      "description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}