The Influence Of Ss-Quasinormal Subgroup On The Structure Of Finite Groups

A subgroup H of G is said to be an ss-quasinormal subgroup of G, if there is a supplement K of H to G such that H permutes with every Sylow subgroup of K. In this paper, by using ss-quasinormal of some special subgroups (such that Sylow subgroups, cyclic subgroups, maximal subgroups of Sylow subgroups )of G. We obtain some sufficient conditions for a finite group to be p-nilpotent, supersolvable.The first chapter, we introduce the investigative background of this paper, and give some definitions and lemmas. The second chapter, we introduces the domestic and abroad research on the situation of the group theory, as well as the background of research. The third chapter, by using the ss-quasinormal of maximal subgroups, some sufficient conditions for a finite group to be p-nilpotent were obtained, which are generalization of some results in correlative papers. The fourth chapter, we use the ss-quasinormal of some subgroups to characterize the structure of groups, obtain some sufficient conditions for supersolvablity of a finite group.