A note on saturated formations (Q757585)

We describe the subgroup-closed saturated formations \({\mathfrak F}\) of finite soluble groups, containing the class \({\mathfrak N}\) of all nilpotent groups, enjoying the following property: If H and K are two \({\mathfrak F}\)- subnormal \({\mathfrak F}\)-subgroups of a finite soluble group \(G=HK\), then G is an \({\mathfrak F}\)-group.