Pro-<i>p</i> groups of positive deficiency

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 × ℤp, with F a finitely generated free pro-p group.

Locations

• Bulletin of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View