We classify the nilpotent finite groups G which are such that the unit
group U(ZG) of the integral group ring ZG has a subgroup of finite in
dex which is the direct product of noncyclic free groups. It is also s
hown that nilpotent finite groups having this property can be characte
rised by means of the Wedderburn decomposition of the rational group a
lgebra QG. (C) 1996 Academic Press, Inc.