Permutation modules for rank 3 unitary groups (Q2266124)

\textit{B. Mortimer} [Proc. Lond. Math. Soc., III. Ser. 41, 1-20 (1980; Zbl 0393.20002)] has analyzed the permutation modules in any characteristic for all known 2-transitive groups. The present author studies the permutation modules of the projective special unitary groups \(PSU(n,q^ 2)\) (n\(\geq 4)\) acting on the set of totally isotropic 1-dimensional subspaces of the underlying n-dimensional vector space over \(GF(q^ 2)\). He is able to determine the complete lattice of submodules in all cases except when the characteristic p of the field divides \(q+1\).