Real Classes of Finite Special Unitary Groups

Abstract

We classify all real and strongly real classes of the finite special unitary group $S{U}_n(q)$. Unless $q\equiv 3(mod4)$ and $n|4$, the classification of real classes is similar to that of the finite special linear group $S{L}_n(q)$. We relate strong reality in $S{U}_n(q)$ to strong reality in the finite special orthogonal groups $S{O}_n^{\pm }(q)$, and we classify real and strongly real classes in the last case for the group $S{O}_n^{\pm }(q)$, when q is odd and $n\equiv 2(mod4)$.

arXiv comment19 pages