Norm group
Encyclopedia
In number theory
, a norm group is a group of the form
where 
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
are precisely the open subgroups of 
of finite index.
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, a norm group is a group of the form
where is a finite abelian extension of nonarchimedean local fieldLocal field
In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non-discrete topology.Given such a field, an absolute value can be defined on it. There are two basic types of local field: those in which the absolute value is archimedean and...
s. 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.