On Oliver's P-group Conjecture

This paper mainly focuses on the problem of Oliver p-group conjecture.This paper is divided into three parts:The first part is the introduction,which mainly introduces the existing results of the Oliver's p-group conjecture,and gives some conclusions of this paper.The second part is the preliminaries,which introduce the basic knowledge of group theory involved in the paper and the relevant knowledge of the finite p-groups.The third part first introduces the Oliver's p-group conjecture:Let p be an odd prime number,and S is a finite p-group,then J(S)?X(S),where J(S)denotes the Thompson subgroup of group S,X(S)denotes the Oliver subgroup of group S.We reviewed some results of the conjecture:The conjecture holds when the nilpotent class of S/X(S)is less than or equal to 4;the conjecture holds when S is the Sylow p-subgroup of GLn(Fq)or Sn.On this basis,this paper verifies that Oliver's p-group conjecture still holds for the Sylow p-subgroups of several small-order classical groups.