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

School of Fundamental Science and Engineering

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

Abstract

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.

Original language	English
Pages (from-to)	166-187
Number of pages	22
Journal	Nagoya Mathematical Journal
Volume	237
DOIs	https://doi.org/10.1017/nmj.2018.16
Publication status	Published - 2020 Mar 1

ASJC Scopus subject areas

Mathematics(all)

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abstract = "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.",

author = "Sosuke Sasaki",

year = "2020",

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doi = "10.1017/nmj.2018.16",

language = "English",

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pages = "166--187",

journal = "Nagoya Mathematical Journal",

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