{
  "id": "1608.03224",
  "version": "v1",
  "published": "2016-08-10T16:11:33.000Z",
  "updated": "2016-08-10T16:11:33.000Z",
  "title": "On weakly $sigma$-permutable subgroups of finite groups",
  "authors": [
    "Chi Zhang",
    "Zhenfeng Wu",
    "W. Guo"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a finite group and {\\sigma} = {{\\sigma}_i, i \\in I} be a partition of the set of all primes \\mathbb{P}. A set \\mathcal{H} of subgroups of G with 1 \\in \\mathcal{H} is said to be a complete Hall {\\sigma}-set of G if every non-identity member of \\mathcal{H} is a Hall {\\sigma}_i-subgroup of G. A subgroup H of G is said to be {\\sigma}-permutable if G possesses a complete Hall {\\sigma}-set \\mathcal{H} such that HA^x = A^xH for all A \\in \\mathcal{H} and all x \\in G. We say that a subgroup H of G is weakly {\\sigma}-permutable in G if there exists a {\\sigma}-subnormal subgroup T of G such that G = HT and H \\cap T \\leq H_{\\sigma}G. where H_{\\sigma}G is the subgroup of H generated by all those subgroups of H which are {\\sigma}-permutable in G. By using this new notion, we establish some new criterias for a group G to be a {\\sigma}-soluble and supersoluble, and also we give the conditions under which a normal subgroup of G is hypercyclically embedded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T16:11:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "permutable subgroups",
      "complete hall",
      "normal subgroup",
      "non-identity member"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}