Isomorphic semisimple group algebras. (English) Zbl 0964.20001

In this short note the author announces without proofs positive results about the isomorphism of semisimple group algebras. The first result concerns group algebras of \(p\)-mixed splitting Abelian groups over a ring of characteristic zero in which \(p\) is not a unit. The second result states that a finitely generated torsion-free metabelian group can be determined up to isomorphism from its group algebra over a fixed field.


20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
16S34 Group rings
20F16 Solvable groups, supersolvable groups
20K21 Mixed groups
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras