FACTORIZATIONS OF THE GROUPS $Ω_{7}(q)$ - Gentcheva, Elenka; Gentchev, Tsanko (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1998)
The following result is proved: Let $G=Ω_{7}(q)$ and $q$ is odd. Suppose that $G = AB$, where $A,B$ are proper non-Abelian simple subgroups of $G$. Then one of the following holds: (1) $q = 3 and A \cong L_{4}(3) or G_{2}(3), B \cong Sp_{6}(2) or A_{9} ;$ (2) $q \equiv -1 (mod 4) and A \cong G_{2}(q), B \cong L_{4}(q); $ (3) $q \equiv 1 (mod 4) and A \cong G_{2}(q), B \cong U_{4}(q); $ (4) $q = 3^{2n+1} > 3 and A \cong \text{ }^{2}G_{2}(q), B \cong L_{4}(q); $ (5) $q = 3^{2n+1} and A \cong U_{3}(q), B \cong L_{4}(q); $ (6) $q = 3^{2n} and A \cong L_{3}(q), B \cong U_{4}(q); $ (7) $A \cong G_{2}(q), B \cong PSp_{4}(q). $