{
  "id": "math/0210190",
  "version": "v1",
  "published": "2002-10-13T18:02:34.000Z",
  "updated": "2002-10-13T18:02:34.000Z",
  "title": "On HNN-extensions in the class of groups of large odd exponent",
  "authors": [
    "S. V. Ivanov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "A sufficient condition for the existence of HNN-extensions in the class of groups of odd exponent $n \\gg 1$ is given in the following form. Let $Q$ be a group of odd exponent $n > 2^{48}$ and $\\mathcal G$ be an HNN-extension of $Q$. If $A \\in \\mathcal G$ then let $\\mathcal F(A)$ denote the maximal subgroup of $Q$ which is normalized by $A$. By $\\tau_A$ denote the automorphism of $\\mathcal F(A)$ which is induced by conjugation by $A$. Suppose that for every $A \\in \\mathcal G$, which is not conjugate to an element of $Q$, the group $<\\tau_A, \\mathcal F(A)>$ has exponent $n$ and, in addition, equalities $A^{-k} q_0 A^{k} = q_k$, where $q_k \\in Q$ and $k =0, 1, ..., [2^{-16}n]$ ($[2^{-16}n]$ is the integer part of $2^{-16}n$), imply that $q_0 \\in \\mathcal F(A)$. Then the group $Q$ naturally embeds in the quotient $\\mathcal G / \\mathcal G^n$, that is, there exists an analog of the HNN-extension $\\mathcal G$ of $Q$ in the class of groups of exponent $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-13T18:02:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20F50",
      "20F05",
      "20F06"
    ],
    "keywords": [
      "large odd exponent",
      "hnn-extension",
      "integer part",
      "maximal subgroup",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10190I"
    }
  }
}