Abstract: Let $n$ denote either a positive integer or infinity, let $\ell$ be a fixed prime and let $K$ be a field of characteristic different from $\ell$. In the presence of sufficiently many roots of unity in $K$, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal $(\mathbb{Z}/\ell^n)$-abelian Galois group (resp. pro-$\ell$-abelian Galois group) of K using the maximal $(\mathbb{Z}/\ell^N)$-abelian-by-central Galois group (resp. pro-$\ell$-abelian-by-central Galois group) of $K$, whenever $N$ is sufficiently large relative to $n$.