{
  "id": "2212.03104",
  "version": "v1",
  "published": "2022-12-04T13:49:25.000Z",
  "updated": "2022-12-04T13:49:25.000Z",
  "title": "On LC-subgroup of a periodic group",
  "authors": [
    "M. Amiri",
    "I. Kashuba",
    "I. Lima"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "As a natural continuation of study $LCM$-groups, we explore other properties of $LCM$-groups and $LC$-series. We obtain some characterizations of finite groups which are not LCM-groups but all proper sections are $LCM$-groups. Also, for a $p$-group $G$, we prove that $G$ is a $LC$-nilpotent group and we obtain a bound for its $LC$-nilpotency. Finally, as an application, we prove that a finite supersolvable group, groups of order $pq, pq^2$ and $pqr$ are $LC$-nilpotent groups, where $p,q$ and $r$ are prime numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-04T13:49:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic group",
      "nilpotent group",
      "lc-subgroup",
      "finite groups",
      "proper sections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}