{
  "id": "1702.00561",
  "version": "v1",
  "published": "2017-02-02T07:35:04.000Z",
  "updated": "2017-02-02T07:35:04.000Z",
  "title": "Autocommuting probability of a finite group",
  "authors": [
    "Parama Dutta",
    "Rajat Kanti Nath"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and $\\Aut(G)$ the automorphism group of $G$. The autocommuting probability of $G$, denoted by $\\Pr(G, \\Aut(G))$, is the probability that a randomly chosen automorphism of $G$ fixes a randomly chosen element of $G$. In this paper, we study $\\Pr(G, \\Aut(G))$ through a generalization. We obtain a computing formula, several bounds and characterizations of $G$ through $\\Pr(G, \\Aut(G))$. We conclude the paper by showing that the generalized autocommuting probability of $G$ remains unchanged under autoisoclinism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-02T07:35:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "20P05",
      "20F28"
    ],
    "keywords": [
      "finite group",
      "automorphism group",
      "randomly chosen element",
      "randomly chosen automorphism",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}