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For G = PSL(2,p^f) denote by ZG the integral group ring, by V(ZG) the groupof normalized units of ZG and let r be a prime different from p. Using the socalled HeLP-method we prove, that units of r-power order in V(ZG) arerationally conjugate to elements of G. As a consequence we prove, thatsubgroups of prime power order in V(ZG) are rationally conjugate to subgroupsof G, provided p = 2 or f =1.

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