{
  "id": "math/0210191",
  "version": "v1",
  "published": "2002-10-13T18:16:44.000Z",
  "updated": "2002-10-13T18:16:44.000Z",
  "title": "On subgroups of free Burnside groups of large odd exponent",
  "authors": [
    "S. V. Ivanov"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that every noncyclic subgroup of a free $m$-generator Burnside group $B(m,n)$ of odd exponent $n \\gg 1$ contains a subgroup $H$ isomorphic to a free Burnside group $B(\\infty,n)$ of exponent $n$ and countably infinite rank such that for every normal subgroup $K$ of $H$ the normal closure $<K >^{B(m,n)}$ of $K$ in $B(m,n)$ meets $H$ in $K$. This implies that every noncyclic subgroup of $B(m,n)$ is SQ-universal in the class of groups of exponent $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-13T18:16:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E07",
      "20F05",
      "20F50"
    ],
    "keywords": [
      "free burnside group",
      "large odd exponent",
      "noncyclic subgroup",
      "generator burnside group",
      "countably infinite rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10191I"
    }
  }
}