{
  "id": "2106.13866",
  "version": "v1",
  "published": "2021-06-25T19:59:05.000Z",
  "updated": "2021-06-25T19:59:05.000Z",
  "title": "Certain residual properties of HNN-extensions with central associated subgroups",
  "authors": [
    "E. V. Sokolov"
  ],
  "comment": "28 pages, in Russian; an English version will be available soon",
  "categories": [
    "math.GR"
  ],
  "abstract": "Suppose that $G$ is a group, $H$ and $K$ are proper isomorphic central subgroups of $G$, and $\\mathfrak{G}$ is an HNN-extension of $G$ with the associated subgroups $H$ and $K$. We prove necessary and sufficient conditions for $\\mathfrak{G}$ to be residually a $\\mathcal{C}$-group, where $\\mathcal{C}$ is a class of groups closed under taking subgroups, extensions, homomorphic images, and Cartesian products of the form $\\prod_{y \\in Y}X_{y}$, where $X, Y \\in \\mathcal{C}$ and $X_{y}$ is an isomorphic copy of $X$ for each $y \\in Y$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-25T19:59:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26",
      "20E06"
    ],
    "keywords": [
      "central associated subgroups",
      "residual properties",
      "hnn-extension",
      "proper isomorphic central subgroups",
      "cartesian products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}