2-Coverings of classical groups

Abstract

In this paper we show that if $n\geq 5$ and $G$ is any of the groups $SU_n(q)$ with $n\neq 6,$ $Sp_{2n}(q)$ with $q$ odd, $\Omega_{2n+1}(q),$ $\Omega_{2n}^{\pm}(q),$ then $G$ and the simple group $\barG=G/Z(G)$ are not 2-coverable. Moreover the only 2-covering of $Sp_{2n}(q),$ with $q$ even, has components $ O^-_{2n}(q)$ and $O^{+}_{2n}(q) .$