On free products inside the unit group of integral group rings.

We use bicyclic units to give an explicit construction of a subgroup of U Z G isomorphic to the free product of two free abelian groups of rank two, assuming that G is a finite nilpotent group and it contains an element g of odd prime order such that the subgroup 〈 g 〉 is not normal in G. To do this we first construct a subgroup isomorphic to the desired free product inside GL (2 , C) and then we find a nontrivial matrix representation of a subgroup of U Z G generated by some bicyclic units and their conjugations under the involution of Z G. We show that for an arbitrary finite group G our construction need not lead to a free product. At the end we shortly discuss possibility of constructing subgroups isomorphic to the free product of two free abelian groups of rank p − 1 for p > 3 in a similar way. [ABSTRACT FROM AUTHOR]