## Nagoya Mathematical Journal

### An application of Iwasawa theory to constructing fields {${\bf Q}(\zeta\sb n+\zeta\sb n\sp {-1})$} which have class group with large {$p$}-rank

Manabu Ozaki

#### Abstract

Let $p$ be an odd prime number. By using Iwasawa theory, we shall construct cyclotomic fields whose maximal real subfields have class group with arbitrarily large $p$-rank and conductor with only four prime factors.

#### Article information

Source
Nagoya Math. J., Volume 169 (2003), 179-190.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631813

Mathematical Reviews number (MathSciNet)
MR1962527

Zentralblatt MATH identifier
1045.11076

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11R18: Cyclotomic extensions 11R29: Class numbers, class groups, discriminants

#### Citation

Ozaki, Manabu. An application of Iwasawa theory to constructing fields {${\bf Q}(\zeta\sb n+\zeta\sb n\sp {-1})$} which have class group with large {$p$}-rank. Nagoya Math. J. 169 (2003), 179--190. https://projecteuclid.org/euclid.nmj/1114631813

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