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Let $p$ be a prime. We prove that a positive solution to Efrat's ElementaryType Conjecture implies a positive solution to the strengthened version ofMina\v{c}--T\^an's Massey Vanishing Conjecture in the case of finitelygenerated maximal pro-$p$ Galois groups whose pro-$p$ cyclotomic character hastorsion-free image. Consequently, the maximal pro-$p$ Galois group of a field$\mathbb{K}$ containing a root of 1 of order $p$ (and also \sqrt{-1} if $p=2$)satisfies the strong $n$-Massey vanishing property for every $n>2$ (which isequivalent to the cup-defining $n$-Massey product property for every $n>2$, asdefined by Mina\v{c}--T\^an) in several relevant cases.

Massey products in Galois cohomology and the Elementary Type Conjecture