Let P (j) (resp. S(n)(j)) be the subalgebra of the Steenrod algebra Ap (resp. nth Morava stabilizer algebra) generated by reduced powers Ppi , 0 ≤ i ≤ j (resp. ti, 1 ≤ i ≤ j). In this paper we identify the dual P (j − 1)∗ of P (j − 1) (resp. S(n)(j), for j ≤ n) with some Frobenius kernel (resp. Fpn -points) of a unipotent subgroup G(j + 1) of the general linear algebraic group GLj+1. Using thes...

We study the mod p cohomology of the classifying space of the projective unitary group PU(p). We first prove that conjectures due to J.F. Adams and Kono and Yagita (1993) about the structure of the mod p cohomology of the classifying space of connected compact Lie groups hold in the case of PU(p). Finally, we prove that the classifying space of the projective unitary group PU(p) is determined b...