Demuškin-Erzeugende und Einbettungsprobleme für elementar-abelsche 2-Erweiterungen zwei-adischer Zahlkörper (Q788049)

According to Demushkin, Serre, and Labute the Galois group \(D=Gal(k(p)/k)\) of the maximal p-extension k(p) of a local field k over \({\mathbb{Q}}_ p\) has a system of generators with one single defining relation. It remains the problem to describe the action of these generators of a given finite p-extension K/k. This additional information is necessary in order to derive results about embedding problems or about the structure of \(K^{\times}\) as a Gal(K/k)-module. In the case K/k is an elementary Abelian p-extension one can choose the generators in such a way that the projection \(D\to^{res}Gal(K/k)\) has a completely explicit description. In the paper this is shown for a field k over \({\mathbb{Q}}_ 2\) such that \(\sqrt{-1}\not\in k\), a case which was not treated before.