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For an odd prime $p$, we study the image of the Thom map from Brown-Petersoncohomology of $BPU_n$ to the ordinary cohomology in dimensions $0\leq i\leq2p+2$, 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 cohomologyclasses $y_{p,k}\in H^{2p^{k+1}+2}(BPU_n;Z_{(p)})$ are in the image of the Thommap.

On the Brown-Peterson cohomology of $BPU_n$ in lower dimensions and the Thom map