A finiteness theorem for imaginary abelian number fields (Q1353075)

It is an old unsolved problem going back to Euler and his numeri idonei to find all imaginary quadratic number fields with one class per genus. \textit{I. Miyada} [Manuscr. Math. 88, No. 4, 535-540 (1995; Zbl 0851.11061)] recently proved that there are only finitely many complex fields with Galois groups of exponent 2 and one class per genus; in the paper under review, the author shows that this result is true for all complex abelian extensions of \(\mathbb{Q}\). He also remarks that those fields with degree \(\geq 6\) can in principle be explicitly determined.