2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75817Cencelj and Dranishnikov showed that for certain nilpotent groups $G$, $K(G_{ab},1) \in \text{AE}(X)$ is equivalent to $K(G,1) \in \text{AE}(X)$ for any compacta $X$ (here $G_{ab}$ is the abelianization of $G$). We examine the same problem for solvable groups. We also give an elementary proof of this fact for any nilpotent group and any 2-dimensional metric space.9 pagesGeometric Topology16B50, 18D35, 54C56text