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June 2021 On the Class Group of an Imaginary Cyclic Field of Conductor $8p$ and $2$-power Degree
Humio ICHIMURA, Hiroki Sumida-TAKAHASHI
Tokyo J. Math. 44(1): 157-173 (June 2021). DOI: 10.3836/tjm/1502179326

Abstract

Let $p=2^{e+1}q+1$ be an odd prime number with $2 \nmid q$. Let $K$ be the imaginary cyclic field of conductor $p$ and degree $2^{e+1}$. We denote by $\mathcal{F}$ the imaginary quadratic subextension of the imaginary $(2,\,2)$-extension $K(\sqrt{2})/K^+$ with $\mathcal{F} \neq K$. We determine the Galois module structure of the $2$-part of the class group of $\mathcal{F}$.

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Humio ICHIMURA. Hiroki Sumida-TAKAHASHI. "On the Class Group of an Imaginary Cyclic Field of Conductor $8p$ and $2$-power Degree." Tokyo J. Math. 44 (1) 157 - 173, June 2021. https://doi.org/10.3836/tjm/1502179326

Information

Published: June 2021
First available in Project Euclid: 7 January 2021

Digital Object Identifier: 10.3836/tjm/1502179326

Subjects:
Primary: 11R18
Secondary: 11R23

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

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Vol.44 • No. 1 • June 2021
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