{
  "id": "2308.14351",
  "version": "v1",
  "published": "2023-08-28T06:53:32.000Z",
  "updated": "2023-08-28T06:53:32.000Z",
  "title": "An axiomatization for the universal theory of the Heisenberg group",
  "authors": [
    "Anthony M. Gaglione",
    "Dennis Spellman"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "The Heisenberg group, here denoted $H$, is the group of all $3\\times 3$ upper unitriangular matrices with entries in the ring $\\mathbb{Z}$ of integers. A.G. Myasnikov posed the question of whether or not the universal theory of $H$, in the language of $H$, is axiomatized, when the models are restricted to $H$-groups, by the quasi-identities true in $H$ together with the assertion that the centralizers of noncentral elements be abelian. Based on earlier published partial results we here give a complete proof of a slightly stronger result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-28T06:53:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal theory",
      "heisenberg group",
      "axiomatization",
      "upper unitriangular matrices",
      "earlier published partial results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}