  For finitely generated groups $H$ and $G$, we observe that $H$ admits a
translation-like action on $G$ implies there is a regular map, which was
introduced in Benjamini, Schramm and Tim\'{a}r's joint paper, from $H$ to $G$.
Combining with several known obstructions to the existence of regular maps, we
have various applications. For example, we show that the Baumslag-Solitar
groups do not admit translation-like actions on the classical lamplighter
group.
