2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105059Let $E$ be a quasilocal field, $R/E$ a finite separable extension, and $R _{\rm ab}$ the maximal abelian subextension of $E$ in $R$. The main result of this paper shows that the norm groups $N(R/E)$ and $N(R_{\rm ab}/E)$ are equal, if the natural Brauer group homomorphism Br$(E) \to $ Br$(L)$ is surjective, for every finite extension $L$ of $E$. The paper proves in a strong form that the surjectivity of the homomorphisms Br$(E) \to $ Br$(L)$ is essential.20 pages, Plain TexRings and AlgebrasNumber Theory11S31, 12F10 (Primary) 12J10 (Secondary)text