On ?-embedded,S?-embedded And H-permutable Subgroups And LA-semigroups

The main motivation behind our work is to investigate the structure of finite groups by using some embedded subgroups and supplemented subgroups.This dissertation consists of several problems in the theory of groups and left almost semigroups.All groups considered in this dissertation are finite.The dissertation comprises the following six chapters.Chapter ? contains a research background and main results of this dissertation.In chapter ?,we list some basic concepts and notions in details.In addition,frequently used conclusions are included.Chapter ? is devoted to study the influence of a-embedded subgroups and a-n-embedded subgroups on the structure of finite groups.We study the structure of finite groups under the assumption that maximal subgroups of Hall ?i-subgroups of finite groups are ?-embedded subgroups or ?-n-embedded subgroups.In particular,a new characterization of hypercyclical embeddability of a normal subgroup of a finite group is obtained based on the notion of?-n-embedded subgroups and some previously known results are generalized.In Chapter ?,we introduce the concept of S?-embedded subgroups in finite groups and investigate their influences on the structure of finite groups.By using the S?-embedded subgroups,we obtain the conditions under which a group is p-nilpotent or a group belongs to some saturated formation containing all supersoluble groups.In particular,for the formation(?)of all supersoluble groups,we establish the conditions under which a normal subgroup of a finite group G is contained in Z(?)(G).In Chapter ?,we establish the theory of weakly(?)-permutable subgroups in finite groups.By using the weakly(?)-permutable subgroups,we obtain some new criteria for a group G to be ?-soluble and supersoluble,and we also give the conditions under which a normal subgroup of G is hypercyclically embedded.Chapter VI aims to generalize the(m,n)-ideals by converting it from an associative ordered structure into a non-associative ordered structure and introduce the concept of(m,n)-ideals in ordered LA-semigroups.The idea is to deal with the special cases of(m,n)-ideals in ordered LA-semigroup by means of ideals.In addition,we study the(m,n)-regular class of an ordered LA-semigroup in terms of(m,n)-ideals.