Isomorphism of Commutative Group Algebras over all Fields

Abstract

It is argued that the commutative group algebra over each field determines up to an isomorphism its group basis for any of the following group classes: • Direct sums of cocyclic groups • Splitting countable modulo torsion groups whose torsion parts are direct sums of cyclics; • Splitting groups whose torsion parts are separable countable • Groups whose torsion parts are algebraically compact • Algebraically compact groups These give a partial positive answer to the R.Brauer’s classical problem.