The $p$-primary subgroups of the cohomology of $BPU_n$ in dimensions less than $2p+5$

Abstract

Let P Un the projective unitary group of rank n and BP Un its classifying space. For an odd prime p, we extend previous results to a compete description of H s (BP Un; Z) (p) for s < 2p + 5 by showing that the p-primary subgroups of H s (BP Un; Z) are trivial for s = 2p + 3 and s = 2p + 4.