In this paper we study virtual rational Betti numbers of a nilpotent-by-abelian group $G$, where the abelianization $N/N'$ of its nilpotent part $N$ satisfies certain tameness property. More precisely, we prove that if $N/N'$ is $2(c(n-1)-1)$-tame as a $G/N$-module, $c$ the nilpotency class of $N$, then $\mathrm{ vb}_j(G):=\sup_{ M\in\mathcal{ A}_G}\dim_\mathbb{ Q} H_j(M,\mathbb{ Q})$ is finite for all $0\leq j\leq n$, where $\mathcal{ A}_G$ is the set of all finite index subgroups of $G$.
Categories: math.GR