Abstract
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 modulo 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.
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