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Let 푝 be a prime. We produce two new families of pro-푝 groups which are not realizable as absolute Galois groups of fields. To prove this, we use the 1-smoothness property of absolute Galois pro-푝 groups. Moreover, we show in these families, one has several pro-푝 groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of the norm residue theorem), or the vanishing of Massey products in Galois cohomology. [ABSTRACT FROM AUTHOR]

Let 𝔽 be a finite field. We prove that the cohomology algebra H∙ (GΓ, 𝔽) with coefficients in 𝔽 of a right-angled Artin group GΓ is a strongly Koszul algebra for every finite graph Γ. Moreover, H∙ (GΓ, 𝔽) is a universally Koszul algebra if, and only if, the graph Γ associated to the group GΓ has the diagonal property. From this, we obtain several new examples of pro-p groups, for a prime number p, whose continuous cochain cohomology algebra with coefficients in the field of p elements is strongly and universally (or strongly and non-universally) Koszul. This provides new support to a conjecture on Galois cohomology of maximal pro-p Galois groups of fields formulated by J. Mináč et al. [ABSTRACT FROM AUTHOR]