Let G be a finitely presented pro-L group with discrete relations. We prove that the kernel of an epimorphism of G to Z(l) is topologically finitely generated if G does not contain a free pro-L group of rank 2. In the case of pro-p groups the result is due to J. Wilson and E. Zelmanov and does not require that the relations are discrete ([15], [17]). For a prop group G of type FP. we define a homological invariant Sigma(m)(G) and prove that this invariant determines when a subgroup H of G that contains the commutator subgroup G' is itself of type FPm. This generalises work of J. King for Sigma(1)(G) in the case when G is metabelian [9]. Both parts of the paper are linked via two conjectures for finitely presented pro-p groups G without free non-cyclic prop subgroups. The conjectures suggest that the above conditions on G impose some restrictions on Sigma(1)(G) and on the automorphism group of G.1444285296