(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1993)
The following result is proved. Let G be a group of Lie type of Lie rank three over a field of 2 or 3 elements. Suppose that G=AB, where A,B are proper non-Abelian simple subgroups of G. Then one of the following holds: 1) G=L_4(2), A L_3(2), B A_6 or A_7; 2)G=L_4(3), A L_3(3), B S_4(3); 3) G=S_6(2), A L_4(2), B L_2(8) or A U_4(2), B L_2(8) or U_3(3); 4) G=U_6(2), A U_5(2), B S_6(2), U_4(3) or M_22 5) G=U_6(3), A U_5(3), B S_6(3); 6) G=O_7(3), A L_4(3), B U_3(3), G_2(3),S_6(2) or A_9 or A G_2(3), B S_4(3), S_6(2)