单K_3-群的新刻画（英文）

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pqr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.     

用$\tau_e(L_2(16))$刻画$L_2(16)$

Let G be a group and πe(G) the set of element orders of G.Let k∈πe(G) and m k be the number of elements of order k in G.Letτe(G)={mk|k∈πe(G)}.In this paper,we prove that L2(16) is recognizable byτe (L2(16)).In other words,we prove that if G is a group such that τe(G)=τe(L2(16))={1,255,272,544,1088,1920},then G is isomorphic to L2(16).