For which words does isomorphism of 1-relator groups imply automorphic equivalence? – mathoverflow.net

It is easy to see that if two words $w,v\in F_r$ are automorphically equivalent (i.e. $\exists \varphi\in \operatorname{Aut}(F_r)$ such that $\varphi(w)=v$), then the one relator groups $\left\langle ...