Isomorphism of group rings of infinite nilpotent groups (Q1101822)

Let G be a group and let R be an integral domain of characteristic 0 in which no element \(g\neq 1\) of G has order invertible. It is proved that if RG\(\simeq RH\) as R-algebras and G is nilpotent, then so is H. The main result of the paper is that if, in addition, cl(G/TG)\(\leq 5\) or G is metabelian, then \(cl(G)=cl(H)\), where TG is the torsion subgroup of G and cl denotes nilpotency class.