The Description of two Categories of Finite Simple Group

Abstract:In the first reference,the author conjectures to depict the finite compound step simple group with the set of maximal subgroup step: if G is a limited group and M is a finite compound step simple group,so G■M,if and only if,∏s(G)=∏s(M),here∏s(G) refers to the set of maximal subgroup step.The author demonstrates this conjecture is tenable to the compound step simple groups 106 with M as their step.The proof of the two finite simple groups Suzuki infinite series simple group and Mathieu group(M1,(i=11,12,22,23,24))shows that the above conjecture is correct,when depicting two categories of finite simple group with the set of maximal subgroup step.