Study On The Influence Of Conjugacy Class Size To The Structures Of Some Finite Simple Groups

The theory of finite groups plays an important role in algebraic systems,and the quantitative properties of finite groups have a very important effect on the structure of finite groups.In this paper,we first focus on the relationship between the special conjugacy class size of two orthogonal groups O8±(2)and O10±(2)and the group structure.Then we study the influence of the length of conjugacy class of Lie type simple groups L2(p2)on the structure of the group.Finally,we describe a class of simple group G with 17 ∈ π(G)? {2,3,…,17}.This paper is divided into three chapters.In chapter 1,we introduce the research background of this paper.In chapter 2,we give some basic knowledge and professinal lemmas which will be used in this paper.In chapter 3,firstly,two kinds of orthogonal groups O8±(2)and O10±(2)are described by using the order of groups and some special conjugacy class size of groups.Secondly,a class of linear groups L2(p2)is described by using the order and the condition of p2||clG(x)| for every element x of order r ∈ π(G)\{p}.Finally,using the order and some special conjugacy class size of the group,we characterize the group G with 17 ∈ π(G)? {2,3,…,17}.