Proceedings of the Japan Academy, Series A, Mathematical Sciences

The ideal class group of the Z23-extension over the rational field

Kuniaki Horie and Mitsuko Horie

Full-text: Open access

Abstract

Given any prime number l which is a primitive root modulo 529 (=232), we shall prove that the l-class group of the Z23-extension over the rational field is trivial.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 85, Number 10 (2009), 155-159.

Dates
First available in Project Euclid: 2 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.pja/1259763075

Digital Object Identifier
doi:10.3792/pjaa.85.155

Mathematical Reviews number (MathSciNet)
MR2591358

Zentralblatt MATH identifier
1234.11146

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R20: Other abelian and metabelian extensions 11R23: Iwasawa theory

Keywords
Z23-extension ideal class group Iwasawa theory

Citation

Horie, Kuniaki; Horie, Mitsuko. The ideal class group of the Z 23 -extension over the rational field. Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 10, 155--159. doi:10.3792/pjaa.85.155. https://projecteuclid.org/euclid.pja/1259763075


Export citation

References

  • K. Horie, Ideal class groups of Iwasawa-theoretical abelian extensions over the rational field, J. London Math. Soc. (2) 66 (2002), no. 2, 257–275.
  • K. Horie, Primary components of the ideal class group of the $\bold Z\sb p$-extension over $\bold Q$ for typical inert primes, Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 3, 40–43.
  • K. Horie and M. Horie, The narrow class groups of some $\Bbb Z\sb p$-extensions over the rationals, Acta Arith. 135 (2008), no. 2, 159–180.
  • K. Horie and M. Horie, The narrow class groups of the $\mathbb Z_{17}$- and $\mathbb Z_{19}$-extensions over the rational field, Abh. Math. Sem. Univ. Hamburg. (to appear).
  • K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257–258.