The class number one problem for some non-abelian normal CM-fields of degree
F. Lemmermeyer, S. Louboutin, R. Okazaki (1999)
Journal de théorie des nombres de Bordeaux
Similarity:
We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to , the alternating group of degree and order . There are two such fields with Galois group (see Theorem 14) and at most one with Galois group SL (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number .