{
  "id": "1801.09235",
  "version": "v1",
  "published": "2018-01-28T14:15:03.000Z",
  "updated": "2018-01-28T14:15:03.000Z",
  "title": "On one generalization of finite nilpotent groups",
  "authors": [
    "Zhang Chi",
    "Alexander N. Skiba"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ be a partition of the set $\\Bbb{P}$ of all primes and $G$ a finite group. A chief factor $H/K$ of $G$ is said to be $\\sigma$-central if the semidirect product $(H/K)\\rtimes (G/C_{G}(H/K))$ is a $\\sigma_{i}$-group for some $i=i(H/K)$. $G$ is called $\\sigma$-nilpotent if every chief factor of $G$ is $\\sigma$-central. We say that $G$ is semi-${\\sigma}$-nilpotent (respectively weakly semi-${\\sigma}$-nilpotent) if the normalizer $N_{G}(A)$ of every non-normal (respectively every non-subnormal) $\\sigma$-nilpotent subgroup $A$ of $G$ is $\\sigma$-nilpotent. In this paper we determine the structure of finite semi-${\\sigma}$-nilpotent and weakly semi-${\\sigma}$-nilpotent groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-28T14:15:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20D15",
      "20D30"
    ],
    "keywords": [
      "finite nilpotent groups",
      "generalization",
      "chief factor",
      "finite group",
      "nilpotent subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}