3
$\begingroup$

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 $M$?

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.