Homological growth of nilpotent-by-abelian pro-p groups

Abstract

We show that the torsion-free rank of $H_i(M,{\mathbb{Z}}_p)$ has finite upper bound for $i\le m$, where $M$ runs through the pro-$p$ subgroups of finite index in a pro-$p$ group $G$ that is (nilpotent of class $c$)-by-abelian such that $G/N^{\prime }$ is of type $F{P}_{2cm}$.