{
  "id": "1609.08815",
  "version": "v1",
  "published": "2016-09-28T08:40:06.000Z",
  "updated": "2016-09-28T08:40:06.000Z",
  "title": "On $σ$-semipermutable subgroups of finite groups",
  "authors": [
    "Wenbin Guo",
    "Alexander N. Skiba"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ be some partition of the set of all primes $\\Bbb{P}$, $G$ a finite group and $\\sigma (G) =\\{\\sigma_{i} |\\sigma_{i}\\cap \\pi (G)\\ne \\emptyset \\}$. A set ${\\cal H}$ of subgroups of $G$ is said to be a \\emph{complete Hall $\\sigma $-set} of $G$ if every member $\\ne 1$ of ${\\cal H}$ is a Hall $\\sigma_{i}$-subgroup of $G$ for some $\\sigma_{i}\\in \\sigma $ and ${\\cal H}$ contains exact one Hall $\\sigma_{i}$-subgroup of $G$ for every $\\sigma_{i}\\in \\sigma (G)$. A subgroup $H$ of $G$ is said to be: \\emph{${\\sigma}$-semipermutable in $G$ with respect to ${\\cal H}$} if $HH_{i}^{x}=H_{i}^{x}H$ for all $x\\in G$ and all $H_i\\in {\\cal H}$ such that $(|H|, |H_{i}|)=1$; \\emph{${\\sigma}$-semipermutable in $G$} if $H$ is ${\\sigma}$-semipermutable in $G$ with respect to some complete Hall $\\sigma $-set of $G$. We study the structure of $G$ being based on the assumption that some subgroups of $G$ are ${\\sigma}$-semipermutable in $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-28T08:40:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20D15",
      "20D30"
    ],
    "keywords": [
      "finite group",
      "semipermutable subgroups",
      "contains exact",
      "complete hall"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}