On the strong Massey property for number fields

Abstract

Let $n\ge 3$. 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.