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The class number one problem for some non-abelian normal CM-fields of degree $24$

F. Lemmermeyer; S. Louboutin; R. Okazaki — 1999

Journal de théorie des nombres de Bordeaux

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 $𝒜_{4}$ , the alternating group of degree $4$ and order $12$ . There are two such fields with Galois group $𝒜_{4} \times 𝒞_{2}$ (see Theorem 14) and at most one with Galois group SL $_{2} (𝔽_{3})$ (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number $1$ .

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The class number one problem for some non-abelian normal CM-fields of degree 24

The class number one problem for some non-abelian normal CM-fields of degree $24$