On the strong Massey property for number fields

TL;DR

This paper proves that for number fields not containing a primitive p-th root of unity, the absolute and tame Galois groups satisfy the strong n-fold Massey property, extending known results in Galois cohomology.

Contribution

It establishes the strong n-fold Massey property for Galois groups of certain number fields, generalizing previous results and adapting Scholz-Reichardt's proof.

Findings

Galois groups satisfy the strong n-fold Massey property when $ otin K$

Extension of Massey property results to broader classes of number fields

Application of adapted Scholz-Reichardt proof technique

Abstract

Let $n\geq 3$. We show that for every number field $K$ with $\zeta_p \notin K$, the absolute and tame Galois groups of $K$ satisfy the strong $n$-fold Massey property relative to $p$. Our work is based on an adapted version of the proof of the Theorem of Scholz-Reichardt.