Characterization of products of pure subgroups

Characterize the finite Galois extensions of henselian valued fields whose Galois group is a product of pure subgroups.

Background

The paper studies finite Galois extensions whose Galois group decomposes into pure subgroups, with purity meaning that the corresponding fixed-field extension is depth one. The main results derive ramification-ideal bounds and establish stronger conclusions for ramification-adapted decompositions, but they do not characterize when such a product decomposition exists.