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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. 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. | |||
== See also == | |||
*[[Takagi existence theorem]] | |||
== References == | |||
*J.S. Milne, ''Class field theory.'' Version 4.01. | |||
{{numtheory-stub}} | |||
[[Category:Number theory]] | |||
Revision as of 00:37, 24 November 2013
In number theory, a norm group is a group of the form where 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 are precisely the open subgroups of of finite index.
See also
References
- J.S. Milne, Class field theory. Version 4.01.