Infinite Class Field Tower of Some Non-abelian Number Fields

Key Points

• This work aims to generalize Schoof’s theorem and apply it to create non-abelian number fields with infinite class field towers.
• Generalization of Schoof's theorem from 1986
• Construction of Kummer extensions of cyclotomic fields
• Identification of small-size non-abelian number fields based on specific criteria.
• Constructed non-abelian number fields with infinite p-class field towers for p = 3, 5, 7.
• Fields exhibit smaller root discriminants and fewer ramified rational primes.