Finite group with c-normal or s-quasinormally embedded subgroups

If P is a p-group for some prime p we shall write M (P ) to denote the set of all maximal subgroups of P and Md(P ) = {P1, ..., Pd} to denote any set of maximal subgroups of P such that ∩d i=1 Pi = Φ(P ) and d is as small as possible. In this paper, the structure of a finite group G under some assumptions on the c-normal or s-quasinormally embedded subgroups in Md(P ), for each prime p, and Sylow p-subgroups P of G is researched. Some known results are generalized. Key–Words: c-normal subgroup; s-quasinormally embedded subgroup; supersolvable groups; Sylow p-subgroup; Finite groups.