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

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