{
  "id": "math/0509377",
  "version": "v2",
  "published": "2005-09-16T13:24:16.000Z",
  "updated": "2005-09-21T07:58:56.000Z",
  "title": "A Note on the Solvablity of Groups",
  "authors": [
    "Shiheng Li",
    "Wujie Shi"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $M$ be a maximal subgroup of a finite group $G$ and $K/L$ be a chief factor such that $L\\leq M$ while $K\\nsubseteq M$. We call the group $M\\cap K/L$ a $c$\\ns section of $M$. And we define $Sec(M)$ to be the abstract group that is isomorphic to a $c$\\ns section of $M$. For every maximal subgroup $M$ of $G$, assume that Sec($M$) is supersolvable. Then any composition factor of $G$ is isomorphic to $L_2(p)$ or $Z_q$, where $p$ and $q$ are primes, and $p\\equiv\\pm 1(mod 8)$. This result answer a question posed by ref. \\cite{WL}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-21T07:58:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20E28"
    ],
    "keywords": [
      "maximal subgroup",
      "ns section",
      "solvablity",
      "result answer",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9377L"
    }
  }
}