UNIT GROUPS OF INTEGRAL GROUP-RINGS

Let U(ZG) be the unit group of the integral group ring ZG. A group G satisfies (*) if either the set T(G) of torsion elements of G is a central subgroup of G or, otherwise, if x is an element of G does not;centralize T(G),then for every t is an element of T(G), x(-1)tx=t(-1). This property appears quite frequently while studying U(ZG). In this paper we investigate why one encounters this property and we have also given a ''unified proof' for some known results regarding this property. Further, some additional results have been obtained.