On subdirect products of free pro-\(p\) groups and Demushkin groups of infinite depth.
A pro-\(p\) group \(G\) is said to be of type \(\text{FP}_m\) if there is a projective resolution of the trivial \(\mathbb Z_pG\)-module \(\mathbb Z_p\), where all modules up to dimension \(m\) are finitely generated. Here \(\mathbb Z_p\) is the ring of \(p\)-adic integers, and \(\mathbb Z_pG\) is the completed group algebra. In the paper under review the authors classify among others the subdirect products of free and Demushkin pro-\(p\) groups of depth \(\infty\) which have homological type \(\text{FP}_m\) for \(m\geq 2\). Although the model for these investigations is the abstract case (see the paper by \textit{M.~R.~Bridson, J. Howie, C. F. Miller III} and \textit{H. Short} [Geom. Dedicata 92, 95-103 (2002; Zbl 1048.20009)]), they note that the corresponding problem is still open for abstract groups for \(m\geq 3\).
scientific article; zbMATH DE number 6005462
scientific article