  The homology groups introduced by A. Brumer can be used to establish a
criterion ensuring that a profinite $\mathbb{F}_p[[G]]$-module of a pro-$p$
group $G$ has projective dimension $d<\infty$ (cf. Thm. A). This criterion
yields a new characterization of free pro-$p$ groups (cf. Cor. B). Applied to a
semi-direct factor $G\to\mathbb{Z}_p\to G$ isomorphic to $\mathbb{Z}_p$ which
defines a non-trivial end in the sense of A.A. Korenev one concludes that the
closure of the normal closure of the image of $\sigma$ is a free pro-$p$
subgroup (cf. Thm. C). From this result we will deduce a structure theorem (cf.
Thm. D) for finitely generated pro-$p$ groups with infinitely many ends.
