20D10 20D20 20D15 20E28 20F17 Finite group; cover-avoidance property; \(p\)-supersoluble groups; saturated formation Fitting class Stone lattice \(\cal F\) -critical group,\(\cal F\) -maximal subgroup \(\cal F\)-hypercentre \(s\)-permutable group boundary condition distributive lattice formation of finite groups hereditary formation local Fitting class local formation nilpotent group quasinormal group saturated formation soluble group supersolublegroup the lattice of Fitting classes the lattice of formations well \(p\)-embedded group