{
  "id": "1906.09424",
  "version": "v1",
  "published": "2019-06-22T10:13:52.000Z",
  "updated": "2019-06-22T10:13:52.000Z",
  "title": "groups with the same number of centralizers",
  "authors": [
    "K. Khoramshahi",
    "M. Zarrin"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "For any group $G$, let $nacent(G)$ denote the set of all nonabelian centralizers of $G$. Amiri and Rostami in (Publ. Math. Debrecen 87/3-4 (2015), 429-437) put forward the following question: Let H and G be finite simple groups. Is it true that if $|nacent(H)| = |nacent(G)|$, then $G$ is isomorphic to $H$? In this paper, among other things, we give a negative answer to this question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-22T10:13:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "D20"
    ],
    "keywords": [
      "finite simple groups",
      "nonabelian centralizers",
      "isomorphic",
      "negative answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}