用阶分量刻画李型单群G_2(q)(英文)  

Characterization of Lie Type Group G_2(q) by Its Order Components

作　　者：陈贵云[1] 

机构地区：[1]西南师范大学数学系,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2001年第5期503-509,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目 ( 198710 66)

摘　　要：用阶分量刻划单群并证明了李型单群G2 (q)也可由阶分量刻画 .定理 1　设G是有限群 ,M =G2 (q) .若OC(G) =OC(M) ,则G≌M .上述结论统一了如下两个结论 :定理 2　设G是有限群 ｜M =G2 (q)且( 1)｜G｜ =｜M｜( 2 )xe(G) =πe(M)则G ≌M .定理 3　设G是有限群 ,Z(G) =1,M =G2 (q) ,N(G) =N(M) ,则G ≌M .It is proved that simple groups G\-2(q) of Lie type are uniquely determined by their order components. Theorem 1\ Let G be a finite group, M=G\-2(q). If OC(G)=OC(M), then G≌M.\;Theorem 1 generalizes the following theorems:\;Theorem 2\ Let G be a finite group, M=G\-2(q). If \;(1) |G|=|M|;\;(2) π\-e(G)=π\-e(M);then G≌M.\;Theorem 3\ Let G be a finite group with Z(G)=1, M=G\-2(q). If N(G)=N(M), then G≌M.

关 键 词：有限群 单群 阶分量 刻画 李型单群 

分 类 号：O152.1[理学—数学]