Norm subgroup of a local field extension
= Norm subgroup of a local field extension
{title2=$N_{L/K}(L^\times)$}
For a finite extension of local fields $L/K$, its norm subgroup is the image of the <field norm> $N_{L/K}:L^\times\to K^\times$. For an abelian extension, it is the kernel of the induced local Artin map to $\operatorname{Gal}(L/K)$.