Ideal class groups, some computations (Q1345280)

An old result of Hasse states that (with one exception) the class number of an imaginary biquadratic extension \(K/\mathbb{Q}\) is equal to the product of the class numbers of the three intermediate quadratic fields up to a factor \(Q/2\), where \(Q\) is the unit index of \(K\) over the totally real quadratic subfield. The author obtains here such a ``product formula'' (but of a different type) for an imaginary biquadratic extension \(M\) of a totally real number field \(F\) which satisfies some special conditions on ramification and signatures of units. Numerical examples \(M/\mathbb{Q}\) are computed, for which (with additional information) the 2-class group of \(M\) can be determined.