##  [Infinite Class Field Tower](/infinite-class-field-tower) 

  ##  [Infinite Class Field Tower](https://puremath.quantumdictionary.io/infinite-class-field-tower-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A tower of number fields obtained by iteratively taking the Hilbert class field (maximal unramified abelian extension) of the previous level that never stabilizes — i.e., the sequence of class fields is infinite and class numbers do not drop to one uniformly, indicating failure of termination of the class field tower.