| In this dissertation,the influence of some kinds of embedded subgroups on the structure of classes of finite groups is mainly studied.And I not only obtained the detailed characterization of solvable groups?p-supersolvable groups and generalized hypercentre of finite groups,but also,investigated the structure of some classes of non-solvable groups.Every group considered in this dissertation is finite.This dissertation is divided into five chapters.Chapter 1,The introduction.In this chapter,the research background and main results of the dissertation are introduced.Chapter 2,The preliminaries.In this chapter,some basic definitions of group theory related to this dissertation are given.Chapter 3,The influence of Mp-embedded subgroups on the construction of classes of groups.In this chapter,the concept of Mp-embedded subgroups is intro-duced,view from different prime divisors of |G|,i.e.the minimal?second prime divisor?5?7 and the general prime divisor of |G|,the relationship between the com-position factors?solvable groups?p-supersolvable groups?generalized hypercentre and the Mp-embedded subgroups is analized.Further,the structure of non-solvable groups is studied by using Mp-embedded subgroups.Chapter 4,The influence of m-embedded subgroups on the construction of classes of non-solvable groups.In this chapter,the definition of m-embedded sub-groups is given,the structure of finite non-solvable groups and generalized hyper-centre is studied by using m-embedded minimal and maximal subgroups of Sylow subgroups.Also,some results in the literature are generalized.Chapter 5,The influence of M*-supplemented subgroups on the structure of classes of groups.In this chapter,the M*-supplemented subgroups is defined,based on the properties of generalized Fitting subgroup,the construction of sat-urated formation containing u and generalized hypercentre is studied by using M*-supplemented subgroups.Also,some results in the literature are improved. |
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