Oriented graphs, pro-p groups and Massey products in Galois cohomology

Let p be a prime. We characterize the oriented right-angled Artin pro-p groups whose Fₚ-cohomology algebra yields no essential n-fold Massey products for every $n>2$, in terms of the associated oriented graph. Moreover, we show that the Fₚ-cohomology algebra of such oriented right-angled Artin pro-p groups is isomorphic to the exterior Stanley-Reisner Fₚ-algebra associated to the same oriented graph. This work also aims at providing a concrete and group-theoretic introduction to the study of Massey products in Galois cohomology for non-specialists, especially graduate students working in profinite group theory.