On the intersection of functorial non-$\mathfrak{F}$-subgroups in groups with operators

The paper considers the structure of the subgroup associated with the intersection of kernels maximal $A$-admissible subgroups that do not simultaneously belong to the formation $\mathfrak{F}$ and do not contain $\mathfrak{F}$-residuals whose indices have certain restrictions. The main properties of the corresponding generalized Frattini subgroup are established.