Torsion completeness of p-primary components in modular group rings of p-reduced Abelian groups

Let G be a p-reduced Abelian group and R a commutative unital ring of prime characteristic p such that for each natural number i the subring $ R^{p^i } $ R^{p^i } has nilpotent elements. It is shown that if S(RG) is the normalized Sylow p-group in the group ring RG, then S(RG) is torsion-complete if and only if G is a bounded p-group. This strengthens our former results on this subject.