Locally isomorphic algebras and a Hasse principle for split metacyclic groups (Q1084475)

This is a report on the author's doctoral thesis [Univ. Augsburg (1985; Zbl 0593.20001)]. In section 1 he studies for semisimple algebras over number fields the concept of local isomorphy at (almost) every prime. He extends results known for number fields to this more general situation. Then he turns over to the central point of his thesis, where he deals with group algebras over number fields. In section 2 he proves a local- global-principle for group algebras of nilpotent groups of odd order. (A counterexample in section 3 shows, that this Hasse principle does not hold for 2-groups.) For split metacyclic groups he deduces from the isomorphy of the group algebras locally everywhere not merely that the algebras are (globally) isomorphic, but even that the groups themselves are isomorphic.