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

A formation 𝔉 of finite groups has the generalized Wielandt property for residuals, or 𝔉 is a GWP-formation, if the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.