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The class number one problem for some non-abelian normal CM-fields of degree 48
Authors:Ku-Young Chang   Soun-Hi Kwon.
Affiliation:Information Security Basic Research Team, ETRI, 161 Kajong-dong, Yusong-Gu, 305-350, Taejon, Korea ; Department of Mathematics Education, Korea University, 136-701, Seoul, Korea
Abstract:We prove that there is precisely one normal CM-field of degree 48 with class number one which has a normal CM-subfield of degree 16: the narrow Hilbert class field of $mathbb{Q} (sqrt{5}, sqrt{101}, theta )$ with $ theta^3 - theta^2 -5 theta -1=0$.

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