On subdirect products of free pro-p groups and Demushkin groups of infinite depth

We study subdirect products of free and Demushkin pro-p groups of depth ∞ developing theory similar to the abstract case, see Bridson et al. (2002) [4]. Furthermore we classify when a subdirect product has homological type FPm for some m⩾2, a problem still open for abstract groups for m⩾3.