Dominions in Abelian subgroups of metabelian groups

It is proved that a suitable free Abelian group of finite rank is not absolutely closed in the class $\mathcal A^2$ of metabelian groups. A condition is specified under which a torsion-free Abelian group is not absolutely closed in $\mathcal A^2$. Also we gain insight into the question when the dominion in $\mathcal A^2$ of the additive group of rational numbers coincides with this subgroup.