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arXiv · 1407.2959

On Bousfield problem for the class of metabelian groups

Sergei O. Ivanov·Roman Mikhailov
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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.

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Sergei O. Ivanov, Roman Mikhailov. 2014-07-10. On Bousfield problem for the class of metabelian groups. https://arxiv.org/abs/1407.2959

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