# Profinite topology on free metabelian group

Let $M$ be free metabelian group of rank $n$. By work of Coulbois, M is $LERF$ and is not $RZ_2$, that means every finitely generated subgroup of $M$ is closed in the profinite topology of $M$ but the product of two finitely generated subgroups of $M$ may not be closed in the profinite topology of M. My question is the following:

Is there an algorithm to compute the closure of the product of two finitely generated subgroups of $M$?

• I think this is an open problem – Benjamin Steinberg Oct 5 '15 at 22:37