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Twisted conjugacy in dihedral Artin groups II: Baumslag Solitar groups $\mathrm{BS}(n,n)$ (2404.04705v2)
Published 6 Apr 2024 in math.GR and cs.CC
Abstract: 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.
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