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 $u$.
Citation
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
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