Nagoya Mathematical Journal

The 2-ideal class groups of $\Bbb Q(\zeta\sb l)$

Pietro Cornacchia

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Abstract

For prime $l$ we study the structure of the $2$-part of the ideal class group Cl of $\,\mathbb{Q}(\zeta_l)$. We prove that Cl$\, \otimes \,{\mathbb {Z}}_2$ is a cyclic Galois module for all $l < 10000$ with one exception and compute the explicit structure in several cases.

Article information

Source
Nagoya Math. J., Volume 162 (2001), 1-18.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631588

Mathematical Reviews number (MathSciNet)
MR1836130

Zentralblatt MATH identifier
1013.11074

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R18: Cyclotomic extensions 11R27: Units and factorization

Citation

Cornacchia, Pietro. The 2-ideal class groups of $\Bbb Q(\zeta\sb l)$. Nagoya Math. J. 162 (2001), 1--18. https://projecteuclid.org/euclid.nmj/1114631588


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