Nearly SS-quasinormal And (?)_s-quasinormal Subgroups Of Finite Groups

In this dissertation, all groups considered are finite.we investigate nearly S S-quasinormal subgroups and Ss-quasinormal subgroups.A subgroup M of G is called nearly S S-quasinormal subgroups in G if there exists a normal subgroup T of G such that MT≤G and M∩T≤MSSG, where MSSG that is contained in M is some S S-quasinormal subgroup of GS is a formation of finite groups in this dissertation. A subgroup M of a group G is said to be Ss-quasinormal in G if there exists a normal subgroup T of G such that MT is s-permutable in G and (M∩T)MG/MG≤Z∞S(G/MG).This dissertation are five chapters.Chapter Ⅰ, we tell the research background and main results.Chapter Ⅱ, we give some symbol, notations, known results.Chapter Ⅲ, we is devoted to some new criteria of p-nilpotent groups and nilpotent groups by considering nearly S S-quasinormal subgroups.Chapter Ⅳ, we is devoted to some new discriptions on supersoluble groups, p-supersoluble groups and the saturated formation that contain all supersoluble groups by considering nearly S S-quasinormal subgroups.Chapter Ⅴ, we study the influence of Ss-quasinormal subgroups on the structure of Sylow tower groups and obtain two new characterizations of Sylow tower group.