On -unramified extensions over imaginary quadratic fields

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal Pub Date : 2023-11-29 DOI:10.1017/s001708952300037x

Kwang-Seob Kim, Joachim König

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引用次数: 0

Abstract

Let

$n$

be an integer congruent to

$0$

$3$

modulo

$4$

. Under the assumption of the ABC conjecture, we prove that, given any integer

$m$

fulfilling only a certain coprimeness condition, there exist infinitely many imaginary quadratic fields having an everywhere unramified Galois extension of group

$A_n \times C_m$

. The same result is obtained unconditionally in special cases.

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虚二次域上的非分枝扩展

设$n$是一个整数，等于$0$或$3$取$4$的模。在ABC猜想的假设下，证明了给定任意整数$m$满足一定的协素性条件，则存在无穷多个虚二次域，它们具有群$A_n \乘以C_m$的处处无分枝伽罗瓦扩展。在特殊情况下也可以无条件地得到同样的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Glasgow Mathematical Journal 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.