Finiteness conditions on subgroups of profinite p-Poincaré duality groups

For a prime number p let G be a profinite p-PDn group with a closed normal subgroup N such that G/N is a profinite p-PDm group and that Hi(V, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{F} $$\end{document}p) is finite for every open subgroup V of N and all i ≤ [n/2]. Generalising [12, Thm. 3.7.4] we show that m ≤ n and N is a profinite p-PDn − m group.