Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A REMARK ON THE NUMBER OF FROBENIUS CLASSES GENERATING THE GALOIS GROUP OF THE MAXIMAL UNRAMIFIED EXTENSION

  • Received : 2019.01.17
  • Accepted : 2020.03.16
  • Published : 2020.06.25
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Abstract

Assume that K is a number field and Kur is the maximal unramified extension of it. When Gal(Kur/K) is an infinite group. It is known that Gal(Kur/K) is generated by finitely many Frobenius classes of Gal(Kur/K) by Y. Ihara. In this paper, we will give the explicit number of Frobenius classes which generate whole group Gal(Kur/K).

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Acknowledgement

This study was supported by research fund from Chosun University, 2019.

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
  2. J. Neukirch, A. Schmidt and K. Wingberg, Cohomology of number fields. Second edition. Grundlehren der Mathematischen Wissenschaften, 323. Springer-Verlag, Berlin, 2008..