An Erdős-Ko-Rado theorem for the group $$\hbox {PSU}(3, q)$$ PSU ( 3 , q )

Abstract

In this paper we consider the derangement graph for the group $$\mathop {\text {PSU}}(3,q)$$ , where q is a prime power. We calculate all eigenvalues for this derangement graph and use the eigenvalues to prove that $$\mathop {\text {PSU}}(3,q)$$ , under its two-transitive action on a set of size $$q^3+1$$ , has the Erdős-Ko-Rado property and, provided that $$q\ne 2, 5$$ , another property that we call the Erdős-Ko-Rado module property.