## Tohoku Mathematical Journal

### Certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals

Kuniaki Horie

#### 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 $u$.

#### Article information

Source
Tohoku Math. J. (2), Volume 59, Number 2 (2007), 259-291.

Dates
First available in Project Euclid: 18 June 2007

https://projecteuclid.org/euclid.tmj/1182180736

Digital Object Identifier
doi:10.2748/tmj/1182180736

Mathematical Reviews number (MathSciNet)
MR2347423

Zentralblatt MATH identifier
1202.11050

#### Citation

Horie, Kuniaki. Certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals. Tohoku Math. J. (2) 59 (2007), no. 2, 259--291. doi:10.2748/tmj/1182180736. https://projecteuclid.org/euclid.tmj/1182180736

#### References

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