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.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.2959
 Bibcode:
 2014arXiv1407.2959I
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Algebraic Topology
 EPrint:
 31 pages