Sur la capitulation des 2-classes d'idéaux de Q(√d, i)

Der Briefwechsel Hasse - Scholz - Taussky

“…Remmert [268] [14], [215]), Bartholdi [16], Bush [47,48,49], Hajir [107,108], Kuhnt [160], Maire [181,182], D. Mayer [188,189,190,191]), McLeman [193], Nover [231], Steurer [307]. Auch die gruppentheoretische Seite dieses Themenkomplexes wurde ausgiebig untersucht (Magnus [180], Serre [293], Nebelung, [222]).…”

“…Eine Fortsetzung 14) der Minimaldiskriminanten mit bes. Berücksichtigung der Galoisgruppen gedenke ich im Furtwängler-Band der Monatshefte zu veröffentlichen.…”

The distribution of second p-class groups on coclass graphs

“…6,p. 492], and parametrized transfer target type τ (K) = (3 j , 3 j+1 ), (3,9) 2 , (3,3,3) , j ≥ 2, is isomorphic to the unique group G 2j+2,2j+3 0…”

“…to one of the two groups G Similarly, we proved for transfer kernel type E.8, κ(K) = (1, 2, 3, 1), resp. E.9, κ(K) = (2, 2, 3, 1), and parametrized transfer target type τ (K) = (3 j , 3 j+1 ), (3,9) 3 , j ≥ 2, that G 2 3 (K) is isomorphic to the unique group G 2j+2,2j+3 0…”

“…(9, 3). On the one hand, there is the case p = 3 for quadratic fields K = Q( √ D) with 3-class group Cl 3 (K) of type (9,3) or (3,3,3), where extensions in the second layer are of absolute degree 18. From the viewpoint of 3-towers, there are no open problems for complex quadratic fields K of type (3,3,3), since it is known that 3 (K) = ∞ [50,63], that is, G ∞ 3 (K) is always an infinite pro-3 group.…”