{
  "id": "1507.03726",
  "version": "v1",
  "published": "2015-07-14T05:55:52.000Z",
  "updated": "2015-07-14T05:55:52.000Z",
  "title": "On the norm of the centralizers of a group",
  "authors": [
    "Mohammad Zarrin"
  ],
  "comment": "group theory",
  "categories": [
    "math.GR"
  ],
  "abstract": "For any group G, let C(G) denote the intersection of the normal- izers of centralizers of all elements of G. Set C0 = 1. De?ne Ci+1(G)=Ci(G) = C(G=Ci(G)) for i ? 0. By C1(G) denote the terminal term of the ascending series. In this paper, we show that a ?nitely generated group G is nilpotent if and only if G = Cn(G) for some positive integer n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-14T05:55:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "centralizers",
      "set c0",
      "terminal term",
      "intersection",
      "ascending series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703726Z"
    }
  }
}