The determination of subgroups in ideal class groups of real quadratic fields (Q1203889)

The author looks at when certain real quadratic fields have class groups with cyclic subgroups of a certain order. A typical result is: Theorem 8. Let \(m=((z^ n_ 1+t)/4-1)^ 2+t\) with \(t| z^ 4_ 1-4\), \(m\neq 37\), then the class group of \(\mathbb{Q}(\sqrt m)\) contains a cyclic subgroup of order \(n\).