Let R be a commutative ring with unity and let G be a group. The group ring RG has a natural involution that maps each element of G to its inverse. We denote by RG+ the set of symmetric elements under this involution. We study necessary and suffient conditions for RG+ to be commutative or, equivalently, for RG+ to be a subring of RG. We also determine all torsion groups G such that the set of symmetric units of RG is a subgroup, when char(R) is an odd prime number.
© Walter de Gruyter