Torsion-Complete Primary Components in Modular Abelian Group Rings over Certain Rings

Abstract

Suppose that \(G\)  is an abelian p-separable group and \(R\) is a commutative unital ring of prime characteristic \(p.\)  It is proved that if \(R`^{p^i}\) possesses nilpotent elements for each natural number \(i\), then the normalized Sylow p-subgroup \(S(RG)\) in the group ring \(RG\) is torsion-complete if and only if \(G\) is p-bounded. This supplies our recent results from Acta Math. Hung. (1997), Ric. Mat. (2002),Tamkang J. Math. (2003) and Intern. J. Math. and Anal. (2006).