Erdos-Ko-Rado theorem for the group $\textrm{PSU}(3,q)$

Abstract

In this paper we consider the derangement graph for the group $\textrm{PSU}(3,q)$ where $q$ is a prime power. We calculate all eigenvalues for this derangement graph and use these eigenvalues to prove that $\textrm{PSU}(3,q)$ has the Erd\H{o}s-Ko-Rado property and, provided that $q\neq 2, 5$, another property that we call the {\textsl Erd\H{o}s-Ko-Rado module property}.