In this second paper we solve the twisted conjugacy problem for even dihedral Artin groups, that is, groups with presentation $G(m) = \langle a,b \mid {}_{m}(a,b) = {}_{m}(b,a) \rangle$, where $m \geq 2$ is even, and $_{m}(a,b)$ is the word $abab\dots$ of length $m$. Similar to odd dihedral Artin groups, we prove orbit decidability for all subgroups $A \leq \mathrm{Aut}(G(m))$, which then implies that the conjugacy problem is solvable in extensions of even dihedral Artin groups.

翻译：在本文中，我们解决了偶数二面体Artin群的扭曲共轭问题，这类群由表示$G(m) = \langle a,b \mid {}_{m}(a,b) = {}_{m}(b,a) \rangle$定义，其中$m \geq 2$为偶数，且$_{m}(a,b)$是长度为$m$的词$abab\dots$。与奇数二面体Artin群类似，我们证明了所有子群$A \leq \mathrm{Aut}(G(m))$的轨道可判定性，进而表明偶数二面体Artin群的扩张中共轭问题可解。