On arrangements of hypersurfaces and Bloch-Kato pro-p groups

The central theme of this thesis is the study of the Bloch-Kato property among some naturally occurring classes of pro-p groups. This property, originally arising in modern Galois theory, imposes some strong conditions simultaneously on the structure of the Fp-cohomology of a pro-p group G and on the Fp-cohomology of every closed subgroup K ≤ G. In this investigation, we will focus our attention on pro-p groups obtained as the pro-p completion of the fundamental groups of certain hypersurface arrangement complements, specifically arrangements of hyperplanes and toric arrangements. The final part of this thesis is dedicated to a different problem about the interplay between groups and graded Lie algebras associated to strongly central series of subgroups.