Preprint pdf-file

Abstract: Let Γ be a finitely presentable pro-p group with a
nontrivial finitely generated closed normal subgroup N of
infinite index. Then def(Γ) ≤ 1, and if def(Γ)=1
then Γ is a pro-p duality group of dimension 2, N is a
free pro-p group and Γ/N is virtually free. In particular,
if the centre of Γ is nontrivial and def(Γ) ≥ 1,
then def(Γ)=1, cd G ≤ 2 and Γ is virtually a
direct product F × Z_{p}, with F a finitely generated free
pro-p group. |