On the cyclotomic unit group and the ideal class group of a real abelian number field II

Manabu Ozaki

doi:10.1006/jnth.1997.2087

On the cyclotomic unit group and the ideal class group of a real abelian number field II

Manabu Ozaki^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

LetKbe a real abelian number field satisfying certain conditions andK_nthenth layer of the cyclotomic Z_p-extension ofK. We study the relation between thep-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group ofK_n. We give certain sufficient conditions which assure that the above two groups are isomorphic as Galois modules for sufficiently largen. We shall also show that they have the samep-rank for sufficiently largen.

Original language	English
Pages (from-to)	223-232
Number of pages	10
Journal	Journal of Number Theory
Volume	64
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1997.2087
Publication status	Published - 1997 Jun

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jnth.1997.2087

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abstract = "LetKbe a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic Zp-extension ofK. We study the relation between thep-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group ofKn. We give certain sufficient conditions which assure that the above two groups are isomorphic as Galois modules for sufficiently largen. We shall also show that they have the samep-rank for sufficiently largen.",

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AB - LetKbe a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic Zp-extension ofK. We study the relation between thep-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group ofKn. We give certain sufficient conditions which assure that the above two groups are isomorphic as Galois modules for sufficiently largen. We shall also show that they have the samep-rank for sufficiently largen.

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On the cyclotomic unit group and the ideal class group of a real abelian number field II

Abstract

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