Twisted conjugacy in dihedral Artin groups II: Baumslag Solitar groups $\mathrm{BS}(n,n)$

Abstract

In this second paper we solve the twisted conjugacy problem for even dihedral Artin groups, that is, groups with presentation $G(m)=⟨a,b\mid {}_m(a,b)={}_m(b,a)⟩$, where $m\ge 2$ 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 $A\le \mathrm{Aut}(G(m))$, which then implies that the conjugacy problem is solvable in extensions of even dihedral Artin groups.

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