{
  "id": "2202.03746",
  "version": "v1",
  "published": "2022-02-08T09:32:56.000Z",
  "updated": "2022-02-08T09:32:56.000Z",
  "title": "Two-closure of rank 3 groups in polynomial time",
  "authors": [
    "Saveliy V. Skresanov"
  ],
  "comment": "29 pages",
  "categories": [
    "math.GR",
    "cs.CC"
  ],
  "abstract": "A finite 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 $G$. We construct a polynomial-time algorithm which given generators of a rank 3 group computes generators of its 2-closure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-08T09:32:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "05E18"
    ],
    "keywords": [
      "polynomial time",
      "two-closure",
      "finite permutation group",
      "largest permutation group",
      "polynomial-time algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}