Groups of p-absolute Galois type that are not absolute Galois groups

Let p be a prime. We study pro -p groups of p -absolute Galois type, as defined by Lam-Liu-Sharifi-Wake-Wang. We prove that the pro -p completion of the right-angled Artin group associated to a chordal simplicial graph is of p -absolute Galois type, and moreover it satisfies a strong version of the Massey vanishing property. Also, we prove that Demushkin groups are of p -absolute Galois type, and that the free pro -p product - and, under certain conditions, the direct product - of two pro -p groups of p -absolute Galois type satisfying the Massey vanishing property, is again a pro -p group of p -absolute Galois type satisfying the Massey vanishing property. Consequently, there is a plethora of pro -p groups of p -absolute Galois type satisfying the Massey vanishing property that do not occur as absolute Galois groups. (c) 2022 Elsevier B.V. All rights reserved.