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

Abstract

The followinf result is proved

Let $G=PSU_6(q)$ and $G=AB$, where $AB$ are proper non-Abelian simple subgroups of $G$. Then one of the following holds:

(1) $q=2$ and $A \cong M_{22}, B \cong PSU_3(2);$

(2) $q=2$ and $A \cong PSU_4(3), B \cong PSU_3(2)$;

(3) $q=2^n>2, n \not\equiv 2$ (mod 4) and $A \cong PSU_3(q), B \cong G_2(q)$;

(4) $q \not\equiv -1$ (mod 5) and $A \cong PSU_5(q), B \cong PSp_6(q)$