{
  "id": "1702.03150",
  "version": "v1",
  "published": "2017-02-10T12:40:15.000Z",
  "updated": "2017-02-10T12:40:15.000Z",
  "title": "Autocommuting probability of a finite group relative to its subgroups",
  "authors": [
    "Parama Dutta",
    "Rajat Kanti Nath"
  ],
  "comment": "13 pages. arXiv admin note: substantial text overlap with arXiv:1702.00561",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $H \\subseteq K$ be two subgroups of a finite group $G$ and Aut$(K)$ the automorphism group of $K$. The autocommuting probability of $G$ relative to its subgroups $H$ and $K$, denoted by ${\\rm Pr}(H, {\\rm Aut}(K))$, is the probability that the autocommutator of a randomly chosen pair of elements, one from $H$ and the other from Aut$(K)$, is equal to the identity element of $G$. In this paper, we study ${\\rm Pr}(H, {\\rm Aut}(K))$ through a generalization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-10T12:40:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "20P05",
      "20F28"
    ],
    "keywords": [
      "finite group relative",
      "autocommuting probability",
      "automorphism group",
      "randomly chosen pair",
      "identity element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}