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

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• 作者：Kwang-Seob Kim ^{kwang12@kias.re.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11R37 ; secondary ; 11F80 ; 11R29
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：166
• 期：Complete
• 页码：235-249
• 全文大小：352 K

文摘

Let K   be a number field and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16300348&_mathId=si1.gif&_user=111111111&_pii=S0022314X16300348&_rdoc=1&_issn=0022314X&md5=b71f86459e86fd9fa9afa407cb9e7f7e" title="Click to view the MathML source">K_urclass="mathContainer hidden">class="mathCode">$K_{ur}$ be the maximal extension of K that is unramified at all places. In this article, we identify real quadratic number fields K   such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16300348&_mathId=si174.gif&_user=111111111&_pii=S0022314X16300348&_rdoc=1&_issn=0022314X&md5=5bb922883ca726d115f1c2f64ab125b8" title="Click to view the MathML source">Gal(K_ur/K)class="mathContainer hidden">class="mathCode">$\mathrm{Gal}(K_{ur}/K)$ is a finite nonsolvable group under the assumption of the Generalized Riemann Hypothesis. We also explicitly calculate their Galois groups.