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2007 Certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals
Kuniaki Horie
Tohoku Math. J. (2) 59(2): 259-291 (2007). DOI: 10.2748/tmj/1182180736

Abstract

We study, for any prime number $p$, the triviality of certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rational field. Among others, we prove that if $p$ is $2$ or $3$ and $l$ is a prime number not congruent to $1$ or $-1$ modulo $2p^2$, then $l$ does not divide the class number of the cyclotomic field of $p^u$th roots of unity for any positive integer $u$.

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Kuniaki Horie. "Certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals." Tohoku Math. J. (2) 59 (2) 259 - 291, 2007. https://doi.org/10.2748/tmj/1182180736

Information

Published: 2007
First available in Project Euclid: 18 June 2007

zbMATH: 1202.11050
MathSciNet: MR2347423
Digital Object Identifier: 10.2748/tmj/1182180736

Subjects:
Primary: 11R29
Secondary: 11R18, 11R20, 11R23

Rights: Copyright © 2007 Tohoku University

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Vol.59 • No. 2 • 2007
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