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.

See also

• Takagi existence theorem

References

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