## Nagoya Mathematical Journal

### On the Galois module structure of ideal class groups

#### 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 $\mathbb{Q}$.

#### Article information

Source
Nagoya Math. J., Volume 164 (2001), 133-146.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631658

Mathematical Reviews number (MathSciNet)
MR1869098

Zentralblatt MATH identifier
1045.11079

Subjects
Primary: 11R29: Class numbers, class groups, discriminants

#### Citation

Komatsu, Toru; Nakano, Shin. On the Galois module structure of ideal class groups. Nagoya Math. J. 164 (2001), 133--146. https://projecteuclid.org/euclid.nmj/1114631658

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