{
  "id": "2311.11497",
  "version": "v1",
  "published": "2023-11-20T02:48:54.000Z",
  "updated": "2023-11-20T02:48:54.000Z",
  "title": "Transitive and non-transitive subgroups of permutation groups",
  "authors": [
    "Arda Demirhan",
    "Jacob Miller",
    "Yixu Qiu",
    "Thomas J. Tucker",
    "Zheng Zhu"
  ],
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "We treat the problem of finding transitive subgroups G of S_n containing normal subgroups N_1 and N_2, with N_1 transitive and N_2 not transitive, such that G/N_1 is isomorphic G/N_2. We show that such G exist whenever n has a prime factor that also divides the Euler-phi function of n. We show that no such G exist when n = pq for p < q with p not dividing q-1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-20T02:48:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation groups",
      "non-transitive subgroups",
      "containing normal subgroups",
      "euler-phi function",
      "prime factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}