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.

References

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

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Norm group

See also

References