  For an odd prime $p$, we study the image of the Thom map from Brown-Peterson
cohomology of $BPU_n$ to the ordinary cohomology in dimensions $0\leq i\leq
2p+2$, where $BPU_n$ is the classifying space of the projective unitary group
$PU_n$. Also we show that a family of well understood $p$-torsion cohomology
classes $y_{p,k}\in H^{2p^{k+1}+2}(BPU_n;Z_{(p)})$ are in the image of the Thom
map.
