Norm group

In number theory, a norm group is a group of the form [math]\displaystyle{ N_{L/K}(L^\times) }[/math] where [math]\displaystyle{ L/K }[/math] 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 [math]\displaystyle{ K^\times }[/math] are precisely the open subgroups of [math]\displaystyle{ K^\times }[/math] of finite index.

See also

• Takagi existence theorem

References

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