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.
Keywords
Cite
@article{arxiv.2112.06744,
title = {Groups of p-absolute Galois type that are not absolute Galois groups},
author = {Simone Blumer and Alberto Cassella and Claudio Quadrelli},
journal= {arXiv preprint arXiv:2112.06744},
year = {2022}
}
Comments
Final version, as it will appear on JPAA