The Influence Of Weak Pronormality Of Subgroups On The Structure Of Finite Groups

For a long time,the relationship between the partial properties of subgroups and the structure of finite groups is one of the important topics in the study of finite groups theory.In this dissertation,the structure of finite groups is described by the weak pronormality of subgroups.This dissertation is divided into four chapters.In Chapter 1,we present the research background of this dissertation and the main results contained in later chapters.In Chapter 2,we give some basic concepts and common conclusions involved in this dissertation.In Chapter 3,we study the influence of weak pronormality of minimal subgroups on the structure of finite groups.We assume the weakly pronormal of partial minimal subgroups of the generalized Fitting subgroups of a group G in the normalizer of Sylow subgroups.So we obtain some new criteria about a saturated formation containing all supersolvable groups,which generalizes some earlier results.In Chapter 4,we mainly study the influence of the weak pronomality of prime power subgroups on the structure of finite groups.We consider the weak pronor-mality of order |D| and p|D|(1<|D|<|P|)subgroups of Sylow p-subgroups P of the generalized Fitting subgroups.So we get the new criteria of a group belongs to some saturated formation.Meanwhile,the result supplement Asaad’s theorem.