Some new criteria on p-supersolubility of finite groups

A subgroup H of a group G is called n-embedded in G if there exists a normal subgroup T of G，such that HT=HG and H∩T≤HsG, where HsG is the maximum s-quasinormal subgroup of G contained in H. Here, some new criteria on p-supersolubility of finite groups are obtained by n-embedded property of some subgroups.