Abstract:

A subgroup H of a finite group G is said to be SS-quasinormal in G if there exists a subgroup B  of  G such that G=HB and H  permutes with every Sylow subgroup of  B.  In this paper, some conditions for a finite group to be p-nilpotent are given using SS-quasinormality of some abelian subgroups with prime power order, and several known results are generalized and improved. 

Key words: finite group; SS-quasinormal subgroups; p-nilpotent groups