{
  "id": "1609.09802",
  "version": "v1",
  "published": "2016-09-30T16:32:43.000Z",
  "updated": "2016-09-30T16:32:43.000Z",
  "title": "On groups elementarily equivalent to a group of triangular matrices $T_n(R)$",
  "authors": [
    "Alexei Miasnikov",
    "Mahmood Sohrabi"
  ],
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "In this paper we investigate the structure of groups elementarily equivalent to the group $T_n(R)$ of all invertible upper triangular $n\\times n$ matrices, where $n\\geq 3$ and $R$ is a characteristic zero integral domain. In particular we give both necessary and sufficient conditions for a group being elementarily equivalent to $T_n(R)$ where $R$ is a characteristic zero algebraically closed field, a real closed field, a number field, or the ring of integers of a number field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-30T16:32:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "20F16"
    ],
    "keywords": [
      "groups elementarily equivalent",
      "triangular matrices",
      "characteristic zero integral domain",
      "number field",
      "characteristic zero algebraically closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}