Friedl–Löh conjecture on undecidability of the uniform epimorphism problem for virtually abelian groups

Let the uniform epimorphism problem ask, given a finitely presented group $G$ and a finitely generated virtually abelian group $H$, whether there exists an epimorphism from $G$ onto $H$.

Friedl–Löh conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually abelian groups is not decidable.

The paper studies the complexity and decidability of epimorphism problems for several classes of virtually abelian targets, but states that it does not resolve this conjecture.