Unramified extensions of quadratic number fields with certain perfect Galois groups

被引：4

作者：

Konig, Joachim ^{[1
]}

机构：

[1] Korea Natl Univ Educ, Dept Math Educ, Cheongju 28173, South Korea

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 03期

关键词：

Inverse Galois theory; unramified Galois extensions; embedding problems; computational number theory; CONSTRUCTION; POLYNOMIALS; Q(T);

D O I：

10.1142/S1793042123500318

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we provide infinite families of quadratic number fields with everywhere unramified Galois extensions of Galois group SL2(7) and 2 . A(7), respectively. To my knowledge, these are the first instances of infinitely many such realizations for perfect groups which are not generated by involutions, a property which makes them difficult to approach for the problem in question and leads to somewhat delicate local-global problems in inverse Galois theory.

引用

页码：639 / 653

页数：15

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