The class number one problem for some non-abelian normal CM-fields

Abstract

Listen

Translate article

Let N be a non-abelian normal CM-eld of degree 4p; p any odd prime. Note that the Galois group of N is either the dicyclic group of order 4p; or the dihedral group of order 4p: We prove that the (relative) class number of a dicyclic CM-eld of degree 4p is always greater then one. Then, we determine all the dihedral CM-elds of degree 12 with class number one: there are exactly nine such CM-elds.