The involution module of $\mathrm{PSU}_{3}(2^{2f})$

Abstract

For any group $G$ the involutions $\mathcal{I}$ in $G$ form a $G$-set under conjugation. The corresponding $kG$-permutation module $k\mathcal{I}$ is known as the involution module of $G$, with $k$ an algebraically closed field of characteristic two. In this paper we discuss the involution module of the projective special unitary group $\mathrm{PSU}_{3}(4^{f})$.