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

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概要

• 論文の詳細を見る

• 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 $u$.

• 東北大学の論文

著者

• Horie Kuniaki

  Department Of Mathematics Tokai University

• Horie Kuniaki

  Department of Mathematics, Tokai University

関連論文

• The ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals
• Certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals
• The ideal class group of the basic $Z_p$-extension over an imaginary quadratic field
• Primary components of the ideal class group of an Iwasawa-theoretical abelian number field
• Triviality in ideal class groups of Iwasawa-theoretical abelian number fields

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