{
  "id": "1804.04634",
  "version": "v1",
  "published": "2018-04-12T17:06:03.000Z",
  "updated": "2018-04-12T17:06:03.000Z",
  "title": "One application of the $σ$-local formations of finite groups",
  "authors": [
    "Zhang Chi",
    "Alexander N. Skiba"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Throughout this paper, all groups are finite. Let $\\sigma =\\{\\sigma_{i} | i\\in I \\}$ be some partition of the set of all primes $\\Bbb{P}$. If $n$ is an integer, the symbol $\\sigma (n)$ denotes the set $\\{\\sigma_{i} |\\sigma_{i}\\cap \\pi (n)\\ne \\emptyset \\}$. The integers $n$ and $m$ are called $\\sigma$-coprime if $\\sigma (n)\\cap \\sigma (m)=\\emptyset$. Let $t > 1$ be a natural number and let $\\mathfrak{F}$ be a class of groups. Then we say that $\\mathfrak{F}$ is $\\Sigma_{t}^{\\sigma}$-closed provided $\\mathfrak{F}$ contains each group $G$ with subgroups $A_{1}, \\ldots , A_{t}\\in \\mathfrak{F}$ whose indices $|G:A_{1}|$, $\\ldots$, $|G:A_{t}|$ are pairwise $\\sigma$-coprime. In this paper, we study $\\Sigma_{t}^{\\sigma}$-closed classes of finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-12T17:06:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20D15",
      "20D20"
    ],
    "keywords": [
      "finite groups",
      "local formations",
      "application",
      "natural number",
      "throughout"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}