The structure of rank 3 permutation modules for O_{2n}(2) and U_m(2) acting on nonsingular points

Abstract

We study the odd-characteristic structure of permutation modules for the rank 3 natural actions of $O_{2n}^{\pm}(2)$ ($n\geq3$) and $U_{m}(2)$ ($m\geq4$) on nonsingular points of their standard modules.