Abstract
Let $\Omega_n$ be the $n$-th layer of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}$ and $h_n$ the class number of $\Omega_n$. We claim that if $\ell$ is a prime number less than $10^4$, then $\ell$ does not divide $h_n$ for any positive integer $n$.
Citation
Takayuki MORISAWA. "A Class Number Problem in the Cyclotomic $\mathbf{Z}_3$-extension of $\mathbb{Q}$." Tokyo J. Math. 32 (2) 549 - 558, December 2009. https://doi.org/10.3836/tjm/1264170249
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