{
  "id": "1206.0185",
  "version": "v1",
  "published": "2012-06-01T13:51:05.000Z",
  "updated": "2012-06-01T13:51:05.000Z",
  "title": "On partially conjugate-permutable subgroups of finite groups",
  "authors": [
    "V. I. Murashka",
    "A. F. Vasil'ev"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $R$ be a subset of a group $G$. We call a subgroup $H$ of $G$ the $R$-conjugate-permutable subgroup of $G$, if $HH^{x}=H^{x}H$ for all $x\\in R$. This concept is a generalization of conjugate-permutable subgroups introduced by T. Foguel. Our work focuses on the influence of $R$-conjugate-permutable subgroups on the structure of finite groups in case when $R$ is the Fitting subgroup or its generalizations $F^{*}(G)$ (introduced by H. Bender in 1970) and $\\tilde{F}(G)$ (introduced by P. Shmid 1972). We obtain a new criteria for nilpotency and supersolubility of finite groups which generalize some well known results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-01T13:51:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite groups",
      "partially conjugate-permutable subgroups",
      "generalization",
      "work focuses",
      "fitting subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0185M"
    }
  }
}