Torsion units in group rings (Q1199337)

Let \(G\) be a non-torsion group such that the set \(T(G)\) of torsion elements of \(G\) is a subgroup and \(G/T(G)\) be right ordered. Let \(U(KG)\) be the group of units of the group ring \(KG\). If \(Z\) is the ring of integers, then the author proves that the following conditions are equivalent: (1) \(T(U(ZG))\subseteq U(ZT(G))\); (2) \(U(ZG)=U(ZT(G))G\); (3) \(T(G)\) is either Abelian or a Hamiltonian group such that if \(T(G)\) is non-Abelian, \(x\in T(G)\), of odd order \(n\), then the multiplicative order of 2 in \(Z_ n\) is an odd number. Furthermore, let \(K\) be a field of characteristic \(p>0\) and let \(G\) be such that for every finitely generated subgroup \(H\) of \(G\), \(T(G)\) is finite. Then \(T(U(KG))=U(KT(G))\) if and only if \(T(G)\) is an Abelian group having no \(p\)-elements and every idempotent of \(KT(G)\) is central in \(KG\).