On the p-primary subgroups of the cohomology of the classifying spaces of PUn

Let $P{U}_n$ denote the projective unitary group of rank $n$, and let $BP{U}_n$ be its classifying space. We extend our previous results to a description of $H^s(BP{U}_n;\mathbb{Z}{)}_{(p)}$ for $s<2p+9$ by showing that $p$-primary subgroups of $H^s(BP{U}_n;\mathbb{Z})$ is $\mathbb{Z}\mathrm{/}p$ for $s=2p+5$ and are trivial for $s=2p+7$ and $s=2p+8$, where $p$ is an odd prime.