  Let K be a field and \ell be a prime such that char K \neq \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
(\Z/\ell)-abelian resp. pro-\ell-abelian Galois group of K using its
(Z/\ell)-central resp. pro-\ell-central extensions.
