有限单群的一些数量性质

Some quantitative properties of finite simple groups

针对文献中关于素图分类存在的问题,利用单群的孤立点集对其进行了修正,并对原结论给出了一个简洁证明。为了刻画所有的交错单群,采取单群和谱相结合的方法,可知交错单群的谱与其他单群不同。同时,还得到一个有趣的数量结果,即阶能被素数p整除的最小的非交换单群是Al t5或A1(p)。这些成果丰富了有限群的数量刻画这一专题内容。

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.