A Sylow theorem for the integral group ring of PSL(2,q)

For G = PSL(2,p^f) denote by ZG the integral group ring over G and by V(ZG) the group of units of augmentation 1 in ZG. Let r be a prime different from p. Using the so-called HeLP-method we prove that units of r-power order in V(ZG) are rationally conjugate to elements of G. As a consequence we prove that subgroups of prime power order in V(ZG) are rationally conjugate to subgroups of G, if p = 2 or f = 1.