Two families of pro-p groups that are not absolute Galois groups

Abstract

Let $p$ be a prime. We produce two new families of pro-$p$ groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-$p$ groups. Moreover, we show in these families one has one-relator pro-$p$ groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.

References in corpus (6)

• 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
• Four-fold Massey products in Galois cohomology
• Pro-p groups with few relations and Universal Koszulity
• One relator maximal pro-p Galois groups and the Koszulity conjectures

Cited by in corpus (4)

• Groups of p-absolute Galois type that are not absolute Galois groups
• Oriented right-angled Artin pro-$\ell$ groups and maximal pro-$\ell$ Galois groups
• Chasing maximal pro-p Galois groups via 1-cyclotomicity
• Directed graphs, Frattini-resistance, and maximal pro-$p$ Galois groups