{
  "id": "1307.0089",
  "version": "v4",
  "published": "2013-06-29T11:16:20.000Z",
  "updated": "2014-01-07T11:12:06.000Z",
  "title": "On $Π$-supplemented subgroups of a finite group",
  "authors": [
    "Xiaoyu Chen",
    "Wenbin Guo"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1301.6361",
  "categories": [
    "math.GR"
  ],
  "abstract": "A subgroup $H$ of a finite group $G$ is said to satisfy $\\Pi$-property in $G$ if for every chief factor $L/K$ of $G$, $|G/K:N_{G/K}(HK/K\\cap L/K)|$ is a $\\pi(HK/K\\cap L/K)$-number. A subgroup $H$ of $G$ is called to be $\\Pi$-supplemented in $G$ if there exists a subgroup $T$ of $G$ such that $G=HT$ and $H\\cap T\\leq I\\leq H$, where $I$ satisfies $\\Pi$-property in $G$. In this paper, we investigate the structure of a finite group $G$ under the assumption that some primary subgroups of $G$ are $\\Pi$-supplemented in $G$. The main result we proved improves a large number of earlier results.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-01-07T11:12:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20D15",
      "20D20"
    ],
    "keywords": [
      "finite group",
      "supplemented subgroups",
      "large number",
      "chief factor",
      "earlier results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.0089C"
    }
  }
}