Variations of Demushkin Groups that are not Absolute Galois Groups
Group Theory
2026-04-02 v2 K-Theory and Homology
Abstract
We construct two families of examples of pro-p groups, with rather elementary presentations, that do not complete into 1-cyclotomic oriented pro-p groups. These provide brand new examples of pro-p groups that do not occur as maximal pro-p Galois groups of fields containing a root of unity of order p - and thus, as absolute Galois groups. Moreover, we show that these pro-p groups may not be ruled out as maximal pro-p Galois groups employing other cohomological properties that are known to hold for all maximal pro-p Galois groups, such as the triple Massey vanishing property, or the quadraticity of Fp-cohomology.
Cite
@article{arxiv.2603.15464,
title = {Variations of Demushkin Groups that are not Absolute Galois Groups},
author = {Simone Blumer and Claudio Quadrelli},
journal= {arXiv preprint arXiv:2603.15464},
year = {2026}
}