  It was recently proven that all free and many virtually free verbally closed
subgroups are algebraically closed in any group. We establish sufficient
conditions for a group that is an extension of a free non-abelian group by a
group satisfying a non-trivial law to be algebraically closed in any group in
which it is verbally closed. We apply these conditions to prove that the
fundamental groups of all closed surfaces (except the Klein bottle) and almost
all free products of groups satisfying a non-trivial law are algebraically
closed in any group in which they are verbally closed.
