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

Abstract

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.

arXiv commentFinal version, as it will appear on JPAA

References in corpus (10)

• Algebraic invariants for right-angled Artin groups
• Triple Massey products vanish over all fields
• The Kummerian Property and Maximal Pro-$p$ Galois Groups
• Bloch-Kato pro-p groups and locally powerful groups
• The Massey vanishing conjecture for number fields
• On pro-$p$ groups with quadratic cohomology
• Profinite properties of RAAGs and special groups
• Galois-theoretic features for 1-smooth pro-$p$ groups
• Right-angled Artin groups and enhanced Koszul properties
• Two families of pro-p groups that are not absolute Galois groups

Cited by in corpus (4)

• Massey products in Galois cohomology and the Elementary Type Conjecture
• Chasing maximal pro-p Galois groups via 1-cyclotomicity
• Demushkin groups of uncountable rank
• Directed graphs, Frattini-resistance, and maximal pro-$p$ Galois groups