Ein Satz über die Geschlechter relativ-zyklischer Zahlkörper von Primzahlgrad und seine Anwendung auf biquadratisch-bizyklische Körper

AbstractWhereas genera of absolute abelian number fields can be described by norm symbols, this is in general impossible for relative abelian fields. Only in the special case of a relative cyclic field of prime degree we shall obtain a characterization of a certain subgroup of the group of genera by norm symbols. This characterization is applied to generalize Hilbert's notation of “Geschlechter der Hauptart” for fields of type (2, 2), and from these we shall obtain an elementary arithmetical proof for the class number-product formula for imaginary fields of type (2, 2)