Norm group

In number theory, a norm group is a group of the form \( N_{L/K}(L^\times) \) where L/K is a finite abelian extension of nonarchimedean local fields. One of the main theorems in local class field theory states that the norm groups in \( K^\times\)are precisely the open subgroups of \( K^\times \) of finite index.
See also

Takagi existence theorem

References