On the mod p cohomology of BPU(p)


We study the mod p cohomology of the classifying space of the 
projective unitary group PU(p). We first proof that old conjectures 
due to J.F. Adams, and Kono and Yagita about the structure of the 
mod p cohomology of classifying space of connected compact Lie groups 
held in the case of PU(p). Finally, we proof that the classifying space 
of the projective unitary group PU(p) is determined by its mod p 
cohomology as an unstable algebra over the Steenrod algebra for p>3, 
completing previous works of Dwyer, Miller, Wilkerson at prime 2 and 
Broto, Viruel at prime 3.