Factorizations of the groups $PSp_{6}(q)$

Abstract

The following result is proved

Let $G=PSp_e(q)$ and $G=AB$, where $A,B$ are proper non-Abelian simple subgroups of $G$. Then one of the following holds:

(1) $q=2$ and $A\cong U_3(3), B \cong U_4(2)$;

(2) $q=4$ and $A \cong J_2, B \cong U_4(4)$;

(3) $q=2^n$ and $A \cong L_2(q^3), B \cong L_4(q)$ or $U_4(q)$;

(4) $q=2^n>2$ and $A \cong G_2(q), B \cong PSp_4(q), L_4(q)$ or $U_4(q)$