Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A REMARK ON p-CLASS NUMBERS IN CYCLOTOMIC ℤp-EXTENSIONS

  • Received : 2021.09.25
  • Accepted : 2022.02.15
  • Published : 2022.03.25
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Abstract

Let 𝔹p,n be the n-th layer of the cyclotomic ℤp-extension over the rationals. In this note, we will prove that the p-class group of 𝔹p,n is trivial for all n by elementary method.

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Acknowledgement

This study was supported by research funds from Chosun University 2021.

References

  1. Y. Ihara, How many primes decompose completely in an infinite unramified Galois extension of a global field?, J. Math. Soc. Japan 35 (1983), no. 4, 693-709. https://doi.org/10.2969/jmsj/03540693