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.
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Bridson, M.R., Kochloukova, D.H. The torsion-free rank of homology in towers of soluble pro-p groups. Isr. J. Math. 219, 817–834 (2017). https://doi.org/10.1007/s11856-017-1499-6
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DOI: https://doi.org/10.1007/s11856-017-1499-6