UNITS OF GROUP-RINGS

In the first part we give a survey of some recent results on construct ing finitely many generators for a subgroup of finite index in the uni t group of an integral group ring ZG of a finite group G. In the secon d part we consider the class of indecomposable finite groups G which m odule their center Z(G) are a direct product of two copies of the cycl ic group C-p of odd prime order p. In case Z(G) is cyclic, a descripti on of the full unit group is given. In the general case a subgroup of finite index is described.