Fs-Quasinormal Subgroups And Fsn-Subgroups Of Finite Groups

All groups considered in this dissertation are finite.Let F be a class of finite groups and G a group. A subgroup H is said to beFs-quasinormal in G, if there exists a normal subgroup T of G such that HT iss-permutable in G and (H∩T)HG/HG≤ZF∞(G/HG).Let F be a class of finite groups and G a group. H is a Ssn-subgroup of G ifthere exists a normal subgroup T of G such that HT is a subnormal subgroup of Gand (H∩T)HG/HG≤ZF∞(G/HG).This dissertation studies the influence of Fs-quasinormal subgroups、Ssn-subgroup and completely c-semipermutable subgroups on the structure of finite groups.There are five chapters.In Chapter I, we introduce the research background and main results in this thesis.In Chapter II, we introduce some concepts, notations and known results which willbe used frequently in this dissortation.In Chapter III,we study the properties of Fs-quasinormal subgroups and use themto give some new characterizations of soluble groups and supersoluble groups.In Chapter IV, we give definition of Fsn-subgroups and use them to give somenew criteria and sufficient and necessary conditions of soluble groups. Some knownresults are generalized.