On Bousfield problem for the class of metabelian groups
  The homological properties of localizations and completions of metabelian groups are studied. It is shown that, for $R=\mathbb Q$ or $R=\mathbb Z/n$ and a finitely presented metabelian group $G$, the natural map from $G$ to its $R$-completion induces an epimorphism of homology groups $H_2(-,R)$. This answers a problem of A.K. Bousfield for the class of metabelian groups. 
Sergei O. Ivanov and Roman Mikhailov
math.GR math.AT