{
  "id": "2102.08605",
  "version": "v1",
  "published": "2021-02-17T06:55:04.000Z",
  "updated": "2021-02-17T06:55:04.000Z",
  "title": "On factorizations of finite groups",
  "authors": [
    "Mikhail I. Kabenyuk"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and let $\\{A_1,\\ldots,A_k\\}$ be a collection of subsets of $G$ such that $G=A_1\\ldots A_k$ is the product of all the $A_i$ and ${\\rm card}(G)={\\rm card}(A_1)\\ldots{\\rm card}(A_k)$. We shall write $G=A_1\\cdot\\ldots\\cdot A_k$, and call this a $k$-fold factorization of the form $({\\rm card}(A_1),\\ldots,{\\rm card}(A_k))$. We prove that for any integer $k\\geq3$ there exist a finite group $G$ of order $n$ and a factorization of $n=a_1\\ldots a_k$ into $k$ factors other than one such that $G$ has no $k$-fold factorization of the form $(a_1,\\ldots,a_k)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-17T06:55:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60"
    ],
    "keywords": [
      "finite group",
      "fold factorization",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}