Hello,

in their book Cohomology of Finite Groups Adem and Milgram investigate the cohomology of the finite orthogonal and symplectic groups only in case $\mathbb{F}_2$.

Let $p$ be a prime dividing the order of $\text{O}_n(q)$, $\text{Sp}_n(q)$.

I am wondering if anything is known about $\text{H}^\ast(\text{O}_n(q),\mathbb{F}_p)$ or $\text{H}^\ast(\text{Sp}_n(q),\mathbb{F}_p)$.

I am also interested in the maximal elementary abelian $p$-subgroups of these groups In light of Quillen's stratification theorem these two questions are, of course, related to each other.

I would be grateful for any kind of information.

Hello,

in their book Cohomology of Finite Groups Adem and Milgram investigate the cohomology of the finite orthogonal and symplectic groups only in case $\mathbb{F}_2$.

Let $p$ be a prime dividing the order of $\text{O}_n(q)$, $\text{Sp}_n(q)$ and $q$ a prime power.

I am wondering if anything is known about $\text{H}^\ast(\text{O}_n(q),\mathbb{F}_p)$ or $\text{H}^\ast(\text{Sp}_n(q),\mathbb{F}_p)$.

I am also interested in the maximal elementary abelian $p$-subgroups of these groups.

In light of Quillen's stratification theorem these two questions are, of course, related to each other.

I would be grateful for any kind of information.