{
  "id": "1612.01426",
  "version": "v1",
  "published": "2016-12-05T16:43:14.000Z",
  "updated": "2016-12-05T16:43:14.000Z",
  "title": "Groups with finiteness conditions on the lower central series of non-normal subgroups",
  "authors": [
    "Fausto De Mari"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It has been proved in [Arch. Math. (Basel) 86 (2006), p. 310-316] that any locally graded group with finitely many derived subgroups of non-normal subgroups has finite derived subgroup. This result is generalized here, in fact we prove that in a locally graded group $G$ the subgroup $\\gamma_{k}(G)$ is finite when the set $\\{\\gamma_{k}(H)~|~H \\ntriangleleft G \\}$ is finite. Moreover, locally graded groups $G$ for which the set $\\{\\gamma_{k}(H)~|~H\\ntriangleleft G,~H~$infinite$\\}$ is finite are also completely described.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-05T16:43:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F14",
      "20F19"
    ],
    "keywords": [
      "lower central series",
      "non-normal subgroups",
      "finiteness conditions",
      "locally graded group",
      "finite derived subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}