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

• J.S. Milne, Class field theory. Version 4.01.