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December 2008 On the $p$-class Tower of a $\textbf{Z}_{\textrm{p}}$-extension
Ali MOUHIB, Abbas MOVAHHEDI
Tokyo J. Math. 31(2): 321-332 (December 2008). DOI: 10.3836/tjm/1233844054

Abstract

For a number field $k$ and a prime number $p$, let $k_{\infty}$ be a $\textbf{Z}_{\textrm{p}}$-extension of $k$ and $X_{\infty}(k)$ the Galois group over $k_{\infty}$ of the maximal abelian unramified $p$-extension of $k_{\infty}$. We first give a sufficient condition, bearing on the norm index of units in the layers of $k_{\infty}$, for $X_{\infty}(k)$ to be finite. When the prime $p$ is 2 and $X_{\infty}(k)\simeq \textbf{Z}/2\textbf{Z}\times \textbf{Z}/2\textbf{Z}$, we study the structure of the Galois group of the maximal unramified $p$-extension of $k_{\infty}$, improving on some previous results in the case of quadratic fields.

Citation

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Ali MOUHIB. Abbas MOVAHHEDI. "On the $p$-class Tower of a $\textbf{Z}_{\textrm{p}}$-extension." Tokyo J. Math. 31 (2) 321 - 332, December 2008. https://doi.org/10.3836/tjm/1233844054

Information

Published: December 2008
First available in Project Euclid: 5 February 2009

zbMATH: 1209.11095
MathSciNet: MR2477874
Digital Object Identifier: 10.3836/tjm/1233844054

Subjects:
Primary: 11R23
Secondary: 11R11

Rights: Copyright © 2008 Publication Committee for the Tokyo Journal of Mathematics

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Vol.31 • No. 2 • December 2008
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