Zur Berechnung der Kapitulation in bikubischen Zahlkörpern

The capitulation kernel is the kernel of the natural extension homomorphism of the ideal class groups in a extension K|k of number fields. In this paper K is a non-cyclic Galois field of degree 6 over the rationals and k is its quadratic subfield. Two different methods of computing the capitulation kernel are discussed. Both depend on the relationship between capitulation and unit structure. The paper closes with two tables. They contain the capitulation kernel for all ramified extensions K|k having cubic discriminants between –20000 and 100000.