On πF-supplemented,SΦ-embedded,CAP-quasinormal And U-hypercentral Subgroups

This dissertation devotes to study the influences of π(F)-supplemented subgroups.π(F)-embedded subgroups,SΦ-embedded subgroups and CAP-quasinormal subgroups on the structure of finite groups,and to study theU-hypercentrality of normal subgroups.All groups considered in this dissertation are finite.This dissertation is divided into the following five chapters.In Chapter Ⅰ,we introduce the research background and main results of this disser-tation.In Chapter Ⅱ,we list some necessary concepts and frequently-used conclusions.In Chapter Ⅲ,based on the previous studies,we introduce new concepts of π(F)supplemented subgroups and π(F)-embedded subgroups,and discuss their influences on the structure of finite groups.In particular,we obtain some criteria as well as sufficient and necessary conditions for p-nilpotency or supersolubility.Chapter IV aims to further develop the studies of embedded subgroups,and to discuss the applications of Frattini subgroups in the embeddability of subgroups.We establish the theory of CAP-quasinormal subgroups and,SΦ-embedded subgroups,and obtain the conditions under which a group is p-nilpotent or p-supersoluble.or more gen-eral,a group belongs to some saturated formation containing all supersoluble groups.These results unify and generalize many previously known achievements.In Chapter V,we study theU-hypercentrality of normal subgroups by means ofU-Φ-supplemented subgroups and weakly Π-ermbedded subgroups.Particularly,for the formation U of all supersoluble groups,we give the conditions under which a normal subgroup of a finite group G is contained in Z_U(G)or Z_U(G).In addition,some new criteria for p-nilpotency or p-supersolubility are obtained.