Units of group rings

In the first part we give a survey of some recent results on constructing finitely many generators for a subgroup of finite index in the unit group of an integral group ring ZG of a finite group G. In the second part we consider the class of indecomposable finite groups G which module their center Z(G) are a direct product of two copies of the cyclic group C-p of odd prime order p. In case Z(G) is cyclic, a description of the full unit group is given. In the general case a subgroup of finite index is described.