A subgroup H of a finite group G is said to be s-semipermutable if it is permutable with every Sylow p-subgroup of G with We are interested in studying the influence of the s-semipermutability of certain subgroups of prime power order of a finite group on its structure. Some recent results are generalized.

S-quasinormal subgroup, s-semipermutable subgroup, generalized Fitting subgroup, p-nilpotent group, supersolvable group, saturated formation.