On the 2-class group of real multiquadratic fields (Q819866)

This article deals with the \(2\)-class group of multiquadratic number fields. The authors determine all families of such fields with cyclic \(2\)-class groups. Since they show that the \(2\)-rank of the class group is \(\geq 2\) as soon as at least four primes ramify, it is sufficient to study the fields \(\mathbb Q(\sqrt{p_1}, \sqrt{p_2}\,)\) and \(\mathbb Q(\sqrt{p_1}, \sqrt{p_2}, \sqrt{p_3}\,)\) for primes \(p_j \not\equiv 3 \bmod 4\).