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.
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页码：1012 / 1043
页数：32
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