{
  "id": "2001.10247",
  "version": "v1",
  "published": "2020-01-28T10:21:57.000Z",
  "updated": "2020-01-28T10:21:57.000Z",
  "title": "The $D_π$-property on products of $π$-decomposable groups",
  "authors": [
    "L. S. Kazarin",
    "A. Martínez-Pastor",
    "M. D. Pérez-Ramos"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The aim of this paper is to prove the following result: Let $\\pi$ be a set of odd primes. If the group $G=AB$ is the product of two $\\pi$-decomposable subgroups $A=A_\\pi \\times A_{\\pi'}$ and $B=B_\\pi \\times B_{\\pi'}$, then $G$ has a unique conjugacy class of Hall $\\pi$-subgroups, and any $\\pi$-subgroup is contained in a Hall $\\pi$-subgroup (i.e. $G$ satisfies property $D_{\\pi}$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-28T10:21:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D40",
      "20D20",
      "20E32"
    ],
    "keywords": [
      "decomposable groups",
      "unique conjugacy class",
      "satisfies property",
      "odd primes",
      "decomposable subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}