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May 24, 2026International Journal of Number Theory0 citations

Infinite Class Field Tower of Some Non-abelian Number Fields

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QLQi LiuZXZugan Xing

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.

Abstract

We generalize Schoof’s theorem in 1986 and apply it to construct a class of Kummer extensions of cyclotomic fields with an infinite class tower. Moreover, we construct some "small-size" non-abelian number fields with an infinite p-class field tower for p = 3, 5, 7. Here, "small size" is regarded as either a smaller root discriminant, fewer ramified rational primes, or both.

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Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/6a12961548a0ea16656729f8https://doi.org/10.1142/s1793042126501095
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