In [[number theory]], a '''norm group''' is a group of the form <math>N_{L/K}(L^\times)</math> where <math>L/K</math> is a finite [[abelian extension]] of nonarchimedean [[local field]]s, and <math>N_{L/K} </math> is the [[field norm]]. One of the main theorems in [[local class field theory]] states that the norm groups in <math>K^\times</math> are precisely the open subgroups of <math>K^\times</math> of finite [[Index (group theory)|index]].
== See also == *[[Takagi existence theorem]]
== References == *J.S. Milne, ''Class field theory.'' Version 4.01.
[[Category:Algebraic number theory]]
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