title: Norm group
text: # 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.
  
  