单K_3-群的新刻画（英文）

A NEW CHARACTERIZATION OF SIMPLE K_3-GROUPS

本文研究了sn(G)对单K_3-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K_3-群的一个刻画,结果如下:如果|G|=p^2qr且sn(G)={r,,pr,pq},这里p<q<r为不同素数,那么G≌A_5.类似的结论对其它单K_3-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 IGI = p2qr and sn（G） = {r, pr, pq}, where p ≤ q 〈r are different primes, then G ≌ As. And the similar conclusions hold for all the other simple K3-groups.