Bousfield localizations of classifying spaces of nilpotent groups

W. G. Dwyer, E. Dror Farjoun, and D. Ravenel

Let $G$ be a finitely generated nilpotent group. We show that the
localization of $BG$ with respect to a multiplicative complex oriented
homology theory $h_*$ is again a space of type $K(\pi,1)$; in fact, it
is the same as the localization of $BG$ with respect to the ordinary
homology theory determined by the ring $h_0$.