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Let $p$ be a prime. We prove that certain amalgamated free pro-$p$ productsof Demushkin groups with pro-$p$-cyclic amalgam cannot give rise to a1-cyclotomic oriented pro-$p$ group, and thus do not occur as maximal pro-$p$Galois groups of fields containing a root of 1 of order $p$. We show that othercohomological obstructions which are used to detect pro-$p$ groups that are notmaximal pro-$p$ Galois groups - the quadraticity of$\mathbb{Z}/p\mathbb{Z}$-cohomology and the vanishing of Massey products - failwith the above pro-$p$ groups. Finally, we prove that the Mina\v{c}-T\^anpro-$p$ group cannot give rise to a 1-cyclotomic oriented pro-$p$ group, and weconjecture that every 1-cyclotomic oriented pro-$p$ group satisfy the strong$n$-Massey vanishing property for $n>2$.

Chasing maximal pro-p Galois groups via 1-cyclotomicity