Twisted conjugacy in dihedral Artin groups I: Torus Knot groups
<|reference_start|>Twisted conjugacy in dihedral Artin groups I: Torus Knot groups: 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.<|reference_end|>
@article{crowe2024twisted,
    title={Twisted conjugacy in dihedral Artin groups I: Torus Knot groups},
    author={Gemma Crowe},
    journal={arXiv preprint arXiv:2403.16671},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16671},
    primaryClass={math.GR cs.CC}
}