{
  "id": "0910.3463",
  "version": "v1",
  "published": "2009-10-19T05:52:32.000Z",
  "updated": "2009-10-19T05:52:32.000Z",
  "title": "The twisted conjugacy problem for pairs of endomorphisms in nilpotent groups",
  "authors": [
    "V. Roman'kov",
    "E. Ventura"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "An algorithm is constructed that, when given an explicit presentation of a finitely generated nilpotent group $G,$ decides for any pair of endomorphisms $\\varphi, \\psi : G \\to G$ and any pair of elements $u, v \\in G,$ whether or not the equation $(x\\varphi)u = v (x\\psi)$ has a solution $x \\in G.$ Thus it is shown that the problem of the title is decidable. Also we present an algorithm that produces a finite set of generators of the subgroup (equalizer) $Eq_{\\varphi, \\psi}(G) \\leq G$ of all elements $u \\in G$ such that $u \\varphi = u \\psi .$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-19T05:52:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "29F18"
    ],
    "keywords": [
      "twisted conjugacy problem",
      "endomorphisms",
      "finitely generated nilpotent group",
      "finite set",
      "explicit presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.3463R"
    }
  }
}