On formations of finite groups with the generalised Wielandt property for residuals

On one problem in formation theory

“…Then G possesses the above properties (1)- (9). Since G ∈ b(F) and the socle Soc(G) is nonabelian; in particular, property (9) implies that G/G F ∈ M and G F ∈ M. Hence, by property (8), G F = G M is a minimal normal subgroup in G and G M ∈ form(S). Note also that, by property (7) i.e., A F B F is a normal subgroup in A.…”