单K3-群的新刻画

摘要

本文研究了sn(G)对单K3-群的影响.通过对有限群G的子群和主因子的分析,给出了单K3-群的一个刻画,结果如下:如果|G|=p2qr且sn(G)={r,pr,pq},这里p＜q＜r为不同素数,那么G≌A5.类似的结论对其它单K3-群都成立.%In this paper,we study the influence of sn(G) on simple K3-groups.Through the analysis of the subgroups and chief factor of the finite group G,we give a characterization of simple K3-groups and the results are as follows.If |G| =p2qr and sn(G) ={r,pr,pq},where p ＜ q ＜ r are different primes,then G ≌ A5.And the similar conclusions hold for all the other simple K3-groups.