L_4(4)的非交换图刻画  

A Characterization of L_4(4) by Its Noncommuting Graph

作　　者：张良才[1] 施武杰[2] 刘雪峰[3] 

机构地区：[1]重庆大学数学与物理学院,重庆400044 [2]苏州大学数学科学学院,江苏苏州215006 [3]北京科技大学材料科学与工程学院,北京100083

出　　处：《数学年刊（A辑）》2009年第4期517-524,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10871032,No.50674008);教育部新世纪优秀人才支持计划(No.NCET-06-0083);重庆大学横向基金(No.104207520080834,No.104207520080968)资助的项目

摘　　要：令G是一个有限非交换群。如下定义群G的非交换图▽(G):其顶点集是G\Z(G),任意两个顶点x和y相连的充要条件是[x,y]≠1.2006年,Abdollahi A.,Akbari S.和Maimani H.R.提出了如下猜想:若群G满足条件▽(G)≌▽(M),其中M是有限非交换单群,则G≌M.尽管该猜想对于具有非连通素图的有限单群以及交错群A_(10)是成立的,但是人们仍不知道它对于除A_(10)外的具有连通素图的有限单群是否成立。该文证明了上述猜想对于射影特殊线性单群L_4(4)也是成立的。Let G be a nonabelian group and associate a noncommuting graph △（G） with G as follows： The vertex set of △（G） is G／Z（G） with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In 2006, Abdollahi A., Akbari S. and Maimani H. R. put forward a conjecture called AAM＇s Conjecture as follows： If M is a finite nonabelian simple group and G is a group such that △（G） ≌△（M）, then G --- M. Even though this conjecture is known to hold for all simple groups with nonconnected prime graphs and the alternating group A10, it is still unknown for all simple groups with connected prime graphs except A10. It is proved that the conjecture is also true for the projective special linear simple group L4（4）.

关 键 词：有限群 非交换图 AAM猜想 射影特殊线性单群 

分 类 号：O152.1[理学—数学]