{
  "id": "1308.3192",
  "version": "v1",
  "published": "2013-08-14T17:52:21.000Z",
  "updated": "2013-08-14T17:52:21.000Z",
  "title": "On pairs of finitely generated subgroups in free groups",
  "authors": [
    "A. Yu. Olshanskii"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that for arbitrary two finitely generated subgroups A and B having infinite index in a free group F, there is a subgroup H of finite index in B such that the subgroup generated by A and H has infinite index in F. The main corollary of this theorem says that a noncyclic free group of finite rank admits a faithful highly transitive action on an infinite set, whereas the restriction of this action to any finitely generated subgroup of infinite index in F has no infinite orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-14T17:52:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finitely generated subgroup",
      "infinite index",
      "noncyclic free group",
      "finite rank admits",
      "infinite orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.3192O"
    }
  }
}