  It was conjectured by H. Zassenhaus that a torsion unit of an integral group
ring of a finite group is conjugate to a group element within the rational
group algebra. The object of this note is the computational aspect of a method
developed by I.S. Luthar and I.B.S. Passi which sometimes permits an answer to
this conjecture. We illustrate the method on certain explicit examples. We
prove with additional arguments that the conjecture is valid for any
3-dimensional crystallographic point group. Finally we apply the method to
generic character tables and establish a p-variation of the conjecture for the
simple groups PSL(2,p).
