Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2

被引：1

作者：

Benjamin, Elliot ^{[1
]}

Snyder, C. ^{[2
]}

机构：

[1] Capella Univ, Harold Abel Sch Psychol, Minneapolis, MN 55402 USA

[2] UMaine, Dept Math & Stat, Orono, ME 04469 USA

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 238卷

关键词：

Imaginary quadratic field; Hilbert class field; 2-class group; THEOREM;

D O I：

10.1016/j.jnt.2021.10.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine those imaginary quadratic number fields whose 2-class groups have rank 3 and 4-rank <= 2 and such that the 2-class groups of their Hilbert 2-class fields have rank 2. This result, along with previous work, gives a complete determination of all complex quadratic number fields for which the 2-class groups of their 2-class fields have rank at most 2. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：1012 / 1043

页数：32

共 50 条

[31] On the second Hilbert 2-class field of real quadratic number fields with 2-class group isomorphic to (2, 2n), n ≥ 2
Benjamin, E
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (03) : 763 - 788
[32] On the Hilbert 2-Class Field Tower of Some Imaginary Biquadratic Number Fields
Mohamed Mahmoud Chems-Eddin
Abdelmalek Azizi
Abdelkader Zekhnini
Idriss Jerrari
Czechoslovak Mathematical Journal, 2021, 71 : 269 - 281
[33] ON THE HILBERT 2-CLASS FIELD TOWER OF SOME IMAGINARY BIQUADRATIC NUMBER FIELDS
Chems-Eddin, Mohamed Mahmoud
Azizi, Abdelmalek
Zekhnini, Abdelkader
Jerrari, Idriss
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2021, 71 (01) : 269 - 281
[34] Infinite 2-class field towers of some imaginary quadratic number fields
Sueyoshi, Y
ACTA ARITHMETICA, 2004, 113 (03) : 251 - 257
[35] RELATIONS IN THE 2-CLASS GROUP OF QUADRATIC NUMBER FIELDS
Lemmermeyer, F.
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2012, 93 (1-2) : 115 - 120
[36] Correction to: On the rank of the 2-class group of some imaginary biquadratic number fields
A. Mouhib
S. Rouas
Acta Mathematica Hungarica, 2024, 172 : 287 - 287
[37] REAL QUADRATIC NUMBER FIELDS WITH METACYCLIC HILBERT 2-CLASS FIELD TOWER
Essahel, Said
Dakkak, Ahmed
Mouhib, Ali
MATHEMATICA BOHEMICA, 2019, 144 (02): : 177 - 190
[38] 2-CLASS NUMBERS OF SPECIAL QUADRATIC NUMBER FIELDS
BAUER, H
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1972, 252 : 79 - &
[39] DIVISIBILITY BY 16 OF CLASS NUMBER OF QUADRATIC FIELDS WHOSE 2-CLASS GROUPS ARE CYCLIC
YAMAMOTO, Y
OSAKA JOURNAL OF MATHEMATICS, 1984, 21 (01) : 1 - 22
[40] IMAGINARY BICYCLIC BIQUADRATIC FIELDS WITH ELEMENTARY 2-CLASS GROUP
McCall, Thomas M.
Parry, Charles J.
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2005, 5 (01): : 173 - 195

← 1 2 3 4 5 →