DISTRIBUTION of GALOIS GROUPS of MAXIMAL UNRAMIFIED 2-EXTENSIONS over IMAGINARY QUADRATIC FIELDS

Sosuke Sasaki

doi:10.1017/nmj.2018.16

DISTRIBUTION of GALOIS GROUPS of MAXIMAL UNRAMIFIED 2-EXTENSIONS over IMAGINARY QUADRATIC FIELDS

Sosuke Sasaki^*

^*この研究の対応する著者

基幹理工学部

研究成果: Article › 査読

抄録

Let be an imaginary quadratic field with . It is known that the length of the Hilbert -class field tower is at least . Gerth (On 2-class field towers for quadratic number fields with -class group of type , Glasgow Math. J. 40(1) (1998), 63-69) calculated the density of where the length of the tower is ; that is, the maximal unramified -extension is a -extension. In this paper, we shall extend this result for generalized quaternion, dihedral, and semidihedral extensions of small degrees.

本文言語	English
ページ（範囲）	166-187
ページ数	22
ジャーナル	Nagoya Mathematical Journal
巻	237
DOI	https://doi.org/10.1017/nmj.2018.16
出版ステータス	Published - 2020 3月 1

ASJC Scopus subject areas

数学 (全般)

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10.1017/nmj.2018.16

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doi = "10.1017/nmj.2018.16",

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DISTRIBUTION of GALOIS GROUPS of MAXIMAL UNRAMIFIED 2-EXTENSIONS over IMAGINARY QUADRATIC FIELDS

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