On Inaba extensions for two-dimensional local fields of mixed characteristic

The paper is devoted to extensions of higher local fields determined by certain matrix equations introduced by E. Inaba. It is proved that any extension decomposable into a tower of Artin–Schreier extensions can be embedded into an Inaba extension that is a composite of the given extension and another Inaba extension. Next, any $p$-extension with elementary Abelian Galois group can be embedded into an extension with the Galois group isomorphic to a group of unipotent matrices over the field with $p$ elements.