{
  "id": "2403.16671",
  "version": "v2",
  "published": "2024-03-25T12:09:48.000Z",
  "updated": "2024-05-10T09:28:28.000Z",
  "title": "Twisted conjugacy in dihedral Artin groups I: Torus Knot groups",
  "authors": [
    "Gemma Crowe"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.GR",
    "cs.CC"
  ],
  "abstract": "In this paper we provide an alternative solution to a result by Juh\\'{a}sz that the twisted conjugacy problem for odd dihedral Artin groups is solvable, that is, groups with presentation $G(m) = \\langle a,b \\; | \\; _{m}(a,b) = {}_{m}(b,a) \\rangle$, where $m\\geq 3$ is odd, and $_{m}(a,b)$ is the word $abab \\dots$ of length $m$, is solvable. Our solution provides an implementable linear time algorithm, by considering an alternative group presentation to that of a torus knot group, and working with geodesic normal forms. An application of this result is that the conjugacy problem is solvable in extensions of odd dihedral Artin groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-05-10T09:28:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "20F36"
    ],
    "keywords": [
      "torus knot group",
      "odd dihedral artin groups",
      "geodesic normal forms",
      "implementable linear time algorithm",
      "group presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}