Some examples of real quadratic fields with finite nonsolvable maximal unramified extensions

被引：2
|
作者：
Kim, Kwang-Seob [1 ]
机构：
[1] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea
来源：
JOURNAL OF NUMBER THEORY | 2016年 / 166卷
关键词：
Nonsolvable unramified extensions of number fields; Class number one problems;
D O I：
10.1016/j.jnt.2016.01.031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let K be a number field and K-ur be the maximal extension of K that is unramified at all places. In this article, we identify real quadratic number fields K such that Gal(K-ur/K) is a finite nonsolvable group under the assumption of the Generalized Riemann Hypothesis. We also explicitly calculate their Galois groups. (C) 2016 Elsevier Inc. All rights reserved.
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页码：235 / 249
页数：15
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