Pro-p subgroups of profinite completions of 3-manifold groups

Wilton, Henry John ; Zalesskii, P


We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary 3-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass–Serre theory for finitely generated pro-$p$ groups.