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, and $$N_{L/K} $$ is the field norm. 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.