Translator Disclaimer
2001 On the Galois module structure of ideal class groups
Toru Komatsu, Shin Nakano
Nagoya Math. J. 164: 133-146 (2001).

Abstract

Let $K/k$ be a Galois extension of a number field of degree $n$ and $p$ a prime number which does not divide $n$. The study of the $p$-rank of the ideal class group of $K$ by using those of intermediate fields of $K/k$ has been made by Iwasawa, Masley et al., attaining the results obtained under respective constraining assumptions. In the present paper we shall show that we can remove these assumptions, and give more general results under a unified viewpoint. Finally, we shall add a remark on the class numbers of cyclic extensions of prime degree of $\mathbb{Q}$.

Citation

Download Citation

Toru Komatsu. Shin Nakano. "On the Galois module structure of ideal class groups." Nagoya Math. J. 164 133 - 146, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 1045.11079
MathSciNet: MR1869098

Subjects:
Primary: 11R29

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.164 • 2001
Back to Top