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http://dx.doi.org/10.5831/HMJ.2020.42.2.213

A REMARK ON THE NUMBER OF FROBENIUS CLASSES GENERATING THE GALOIS GROUP OF THE MAXIMAL UNRAMIFIED EXTENSION

Jin, Seokho (Department of Mathematics, Chung-Ang University)
Kim, Kwang-Seob (Department of Mathematics, Chosun University)

Publication Information

Honam Mathematical Journal / v.42, no.2, 2020 , pp. 213-218 More about this Journal

Abstract

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

Keywords

Frobenius classes; generators;

Citations & Related Records

Reference

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