The torsion-free rank of homology in towers of soluble pro-p groups

Abstract

We show that for every finitely presented pro-p nilpotent-by-abelian-by-finite group G there is an upper bound on $${\dim _{{\mathbb{Q}_p}}}\left( {{H_1}\left( {M,{\mathbb{Z}_p}} \right){ \otimes _{{\mathbb{Z}_p}}}{\mathbb{Q}_p}} \right)$$ , as M runs through all pro-p subgroups of finite index in G.