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On the Galois module structure of ideal class groups

Published online by Cambridge University Press:  22 January 2016

Toru Komatsu  and
Shin Nakano
Toru Komatsu
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan, trkomatu@comp.metro-u.ac.jp
Shin Nakano
Affiliation:
Department of Mathematics, Gakushuin University, Toshima-ku, Tokyo 171-8588, Japan, shin@math.gakushuin.ac.jp
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Abstract

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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 Q.

Keywords

11R29
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 164 , December 2001 , pp. 133 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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