Some quantitative properties of finite simple groups

There are some errors in the paper.This paper proposes to remedy the errors by independent set of simple groups,and also provides a simple proof.To characterize all alternating simple groups,the method of combining simple group and spectrum is applied.It finds that the spectrum of any alternating simple group is different from other simple groups' spectrum.At the same time,an interesting result is obtained,which is the smallest non-abelian simple groups whose order can be divided by prime p is Alt5 or A1(p).The results in this study enrich the arithmetic properties of finite groups.