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.

翻译：本文提供了对Juhász关于奇二面体阿廷群中扭曲共轭问题可解性结果的另一种解法，即具有展示$G(m) = \langle a,b \; | \; _{m}(a,b) = {}_{m}(b,a) \rangle$（其中$m\geq 3$为奇数，且$_{m}(a,b)$是长度为$m$的词$abab \dots$）的群是可解的。本文通过考虑环面纽结群的另一种群展示，并利用测地线范式，给出了一个可实现的线性时间算法。该结果的一个应用是：奇二面体阿廷群的扩张中，共轭问题是可解的。