Fundamental unit system and class number of real bicyclic biquadratic number fields

Abstract

In this note, we study the unit groups and class numbers of three classes of bicyclic biquadratic number fields. Following Wada and Zhang's methods, the unit group and class number of a bicyclic biquadratic number field can be represented by the fundamental units and class numbers of their quadratic subgroups. The reason why this method works in our case is that the fundamental unit of the quadratic subfields of our bicyclic biquadratic fields can be determined explicitly.