Algebraic investigations of Hilbert’s theorem 94, the principal ideal theorem and the capitulation problem. (English) Zbl 0704.11048

The paper circles in great detail around the three topics mentioned in its title, it also includes a review of the historical background. Hilbert’s Theorem 94 is shown for general unramified abelian extensions by making use of a generalization of Herbrand’s Lemma. A complete proof of the Principal Ideal Theorem follows; an example from group theory suggests that the two results are independent. The Capitulation Problem finally is treated by studying transfers for groups as well as capitulation genera of unramified abelian extensions.
Reviewer: J.Ritter


11R37 Class field theory
11R20 Other abelian and metabelian extensions
11R29 Class numbers, class groups, discriminants