LAUSR

Abstract A subgroup H of a finite group G is said to be nearly s-embedded in G if G has an s-permutable subgroup T and an s-semipermutable subgroup HssG contained in H such that and , where HsG is the intersection of all s-permutable subgroups of G containing H. In this paper, we present an extension of a result on p-supersolvability of finite groups under the assumption that maximal subgroups of some Sylow p-subgroups are nearly s-embedded. As applications, we give several new criteria for a finite group to be p-nilpotent and supersolvable.