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

Abstract

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 ${\mathit{FP}}_m$ for some $m⩾2$, a problem still open for abstract groups for $m⩾3$.