Norm group explained

In number theory, a norm group is a group of the form

N _{L/K} (L ^{x )} 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 ^{x} are precisely the open subgroups of K ^{x} of finite index.

See also

• Takagi existence theorem

References

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