Some New Characterizations Of Finite ?-Solvable Groups

The relationship between the features of subgroups and the structure of finite groups has always been one of research focus in finite groups.In this paper,we considers structures of finite groups from the aspect of developing the concept of c-normality and cover-avoiding,and then investigate the influence of generalized c#-normal subgroup and generalized semi CAP-subgroup on the 7r-solvability of finite groups by using the method of a combination of induction and counter-example of minimal order is adoptedWe introduce the generalized c#-normal subgroup,which generalize the concept of c-normal subgroups and cover-avoid subgroups.In Chapt,er 3,firstly,we use gen-eralized c#-normality of Hall subgroups to describe the structure of finite 7r-solvable group.Secondly,we use generalized c#-normality of solvability of maximal subgroups,special 2-maximal subgroups and obtain four sufficient and necessary conditions for a group to be solvable.Finally,we consider generalized c#-normality of sylow subgroup of maximal subgroups and 3-maximal subgroups,and then give two sufficient conditions for a group to be solvable.In Chapter 4,we research the structure of finite group by using generalized semi CAP-subgroup of Hall subgroups H,that is,there exists a normal subgroup(s-quasinormal subgroup)K of G such that HK(?)G(HK(?)G)and H?K is a semi CAP-subgroup(including in semi cap-subgroup)of G.And then we obtain some new sufficient conditions for a group to be ?-solvable or ?'-solvable.