用oc(G)刻画单K_3-群  

A Characterization of Simple K_3-Groups by oc(G)

作　　者：戴雪[1] 张庆亮[1] 

机构地区：[1]南通大学理学院,江苏南通226019

出　　处：《西南师范大学学报（自然科学版）》2017年第12期22-25,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11401324;11601245)

摘　　要：若由Γ(H)=Γ(G)可以推出H■G,则称有限群G为素图可刻画的.这方面的成果很多,但是能素图刻画的群并不多.然而,我们发现一些有限群G可以用oc(G)={|CG(x)||x是任意的素数阶元}来刻画.本研究证明了如下结果:若G为有限群且oc(G)=oc(H),则G■H,这里H为单K3-群.A finite group Gis said to be recognizable by aprime graph if the equality Γ（H）=Γ（G） implies that H■G.There are many articles in this area,but not many groups can be recognized by aprime graph.However,we find that some groups can be recognized by oc（G）={｜CG（x）｜｜xis an arbitrary element of prime order}.In the present paper,we obtain the following result.If G be a finite group and oc（G）=oc（H）,then G■H,where His a simple K3-group.

关 键 词：素数阶元的中心化子 素图 单K3-群 

分 类 号：O152.1[理学—数学]