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

TL;DR

This paper investigates the derangement graph of the group PSU(3,q), computes its eigenvalues, and proves it satisfies the Erdős-Ko-Rado property and an additional module property for most q values.

Contribution

It provides the first eigenvalue calculations for the derangement graph of PSU(3,q) and establishes the Erdős-Ko-Rado and module properties for this group.

Findings

Proved PSU(3,q) has the Erdős-Ko-Rado property.

Calculated all eigenvalues of the derangement graph.

Established the Erdős-Ko-Rado module property for q ≠ 2, 5.

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}.