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

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概要

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• For any prime number $p$, we study local triviality of the ideal class group of the ${\boldsymbol Z}_p$-extension over the rational field. We improve a known general result in such study by modifying the proof of the result, and pursue known effective arguments on the above triviality with the help of a computer. Some explicit consequences of our investigations are then provided in the case $p\leq7$.

• 東北大学の論文

著者

• Horie Mitsuko

  Department Of Mathematics Ochanomizu University

• Horie Kuniaki

  Department Of Mathematics Tokai University

• Horie Mitsuko

  Department Of Mathematics Kyushu 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
• Note on the Schur multiplier of a certain semidirect product
• 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
• The Hasse principle for elementary Abelian fields

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