On The Embedded Manner Of Chief Factors And The Structure Of Finite Groups

It is well known that the essence of studying a finite solvable group can be revealed by some "embedding properties" of chief factors in a finite group. The properties of chief factors and the relationship between chief factors and some subgroups in a finite group are widely concerned. In this thesis, we investigate the structure of finite groups under the assumption that some subgroups cover or avoid some chief factors or non-Frattini chief factors of a finite group. Not only many known results are generalized, but also the study of chief factors is perfected.In chapter 3 we investigate the structure of finite groups when some sub-groups have semi cover-avoidance property in a local subgroup. Our results not only enrich some important theorems on chief factors but also generalize some known results including well-known Burnside theorem for finite p-nilpotent groups.In chapter 4 we define the concept of generalized cover-avoidance subgroups, which is a generalization of cover-avoidance subgroups. We obtain some necessary and sufficient conditions for a finite group to be a solvable group, a p-nilpotent group, a supersolvable group and a group contained in a saturated formation when some prime power order subgroups are generalized cover-avoidance subgroups.In chapter 5 we introduce the generalized semi cover-avoidance subgroups and obtain some basic properties. We investigate the solvability of some normal subgroup of a finite group when some maximal subgroups are generalized semi cover-avoidance subgroups.