On duo, reversible and symmetric group rings

Let RG denote the group ring of the torsion group G over a commutative ring R with identity. In this paper we establish some valid implications between the ring-theoretic conditions duo, reversible, SI property and symmetric in the setting of group rings. We further show that if the group ring RG possesses any of these properties, then G is a Hamiltonian group and the characteristic of R is either 0 or 2. Moreover, we characterize the same properties in group rings RG in the following cases: (1) RG is a semi-simple group ring and (2) R is a semi-simple ring and G any group. We prove new results, but also review previous ones.