{
  "id": "1607.03052",
  "version": "v1",
  "published": "2016-07-11T17:33:57.000Z",
  "updated": "2016-07-11T17:33:57.000Z",
  "title": "Linear programming and the intersection of free subgroups in free products of groups",
  "authors": [
    "Sergei V. Ivanov"
  ],
  "comment": "35 pages, 2 figures",
  "categories": [
    "math.GR",
    "math.OC"
  ],
  "abstract": "We study the intersection of finitely generated factor-free subgroups of free products of groups by utilizing the method of linear programming. For example, we prove that if $H_1$ is a finitely generated factor-free noncyclic subgroup of the free product $G_1 * G_2$ of two finite groups $G_1$, $G_2$, then the Walter Neumann coefficient $\\sigma(H_1)$ of $H_1$ is rational and can be computed. This coefficient $\\sigma(H_1)$ is the minimal positive real number such that, for every finitely generated factor-free subgroup $H_2$ of $G_1 * G_2$, it is true that $\\bar {\\rm r}(H_1, H_2) \\le \\sigma(H_1) \\bar {\\rm r}(H_1) \\bar {\\rm r}(H_2)$, where $\\bar {\\rm r} (H) = \\max ( {\\rm r} (H)-1,0)$ is reduced rank of $H$, ${\\rm r}(H)$ is rank of $H$, and $\\bar {\\rm r}(H_1, H_2)$ is reduced rank of a generalized intersection of $H_1, H_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-11T17:33:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20E07",
      "20F65",
      "90C90"
    ],
    "keywords": [
      "free product",
      "free subgroups",
      "linear programming",
      "intersection",
      "finitely generated factor-free subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}