The upper central series of the unit group of an integral group ring

摘要

Let Z(n) (U) denote the n'th term of the upper central series of the unit group U of ZG and (Z) over tilde (U)= U-n=1(infinity) Z(n)(Z). It is shown that if the set of torsion elements of G forms a subgroup T and (Z) over tilde (U)not subset of C-U(T), then T is either an Abelian 2-group or a Q-group. Moreover, (Z) over tilde (U) not subset of G center dot C-U (T) whenever G is an FC group.