Osnel Broche Cristo
Commutativity of symmetric elements in group rings
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.
Journal of Group Theory, Walter de Gruyter
Print ISSN: 1433-5883
Volume: 9, 09/2006
Pages: 673 - 683
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