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.
