{
  "id": "1908.00613",
  "version": "v1",
  "published": "2019-08-01T20:29:24.000Z",
  "updated": "2019-08-01T20:29:24.000Z",
  "title": "Finite Permutation Groups with Few Orbits Under the Action on the Power Set",
  "authors": [
    "Alexander Betz",
    "Max Chao-Haft",
    "Ting Gong",
    "Thomas Michael Keller",
    "Anthony Ter-Saakov",
    "Yong Yang"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The set-transitive groups acting on an $n$ symbol set (i.e. the groups that have $n+1$ set-orbits) have been classified in \\cite{BP55}. In this paper we completely classify the groups with $n+r$ set-orbits for $2 \\leq r \\leq 5$ as well as lay out a method that allows one to go further.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-01T20:29:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite permutation groups",
      "power set",
      "symbol set",
      "set-orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}