{
  "id": "1805.05160",
  "version": "v1",
  "published": "2018-05-14T13:22:20.000Z",
  "updated": "2018-05-14T13:22:20.000Z",
  "title": "Twisted conjugacy classes in unitriangular groups",
  "authors": [
    "Timur Nasybullov"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $R$ be an integral domain of zero characteristic. In this note we study the Reidemeister spectrum of the group ${\\rm UT}_n(R)$ of unitriangular matrices over $R$. We prove that if $R^+$ is finitely generated and $n>2|R^*|$, then ${\\rm UT}_n(R)$ possesses the $R_{\\infty}$-property, i. e. the Reidemeister spectrum of ${\\rm UT}_n(R)$ contains only $\\infty$, however, if $n\\leq|R^*|$, then the Reidemeister spectrum of ${\\rm UT}_n(R)$ has nonempty intersection with $\\mathbb{N}$. If $R$ is a field, then we prove that the Reidemeister spectrum of ${\\rm UT}_n(R)$ coincides with $\\{1,\\infty\\}$, i. e. in this case ${\\rm UT}_n(R)$ does not possess the $R_{\\infty}$-property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-14T13:22:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "twisted conjugacy classes",
      "unitriangular groups",
      "reidemeister spectrum",
      "zero characteristic",
      "nonempty intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}