On Bousfield problem for the class of metabelian groups

Abstract

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.

31 pages