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

For G=PSL(2,pf)G=PSL(2,pf) denote by ZGZG the integral group ring over G   and by V(ZG)V(ZG) the group of units of augmentation 1 in ZGZG. 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)V(ZG) are rationally conjugate to elements of G  . As a consequence we prove that subgroups of prime power order in V(ZG)V(ZG) are rationally conjugate to subgroups of G  , if p=2p=2 or f=1f=1.