On s-Quasinormal and c-Normal Subgroups of a Finite Group

Let ■be a saturated formation containing the class of supersolvable groups and let G be a finite group.The following theorems are shown:(1)G ∈■ if and only if there is a normal subgroup H such that G/H ∈■and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G;(2)G ∈■ if and only if there is a soluble normal subgroup H such that G/H ∈■ and every maximal subgroup of all Sylow subgroups of F(H),the Fitting subgroup of H,is either c-normally or s-quasinormally embedded in G.