关于Thompson猜想与AAM猜想(英文)  

ON THOMPSON’S CONJECTURE AND AAM’S CONJECTURE

作　　者：张良才[1] 施武杰[2] 王玲丽[3] 

机构地区：[1]重庆大学数理学院,重庆400044 [2]苏州大学数学科学学院,江苏苏州215006 [3]中北大学理学院数学系,山西太原030051

出　　处：《数学杂志》2011年第1期28-34,共7页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(10871032);the SRFDP of China(20060285002);a Subproject of the NNSF of China(50674008);Chongqing Univer-sity(104207520080834;104207520080968)

摘　　要：本文研究了有限(几乎)单群的非交换图刻画问题. 利用有限几乎单群的阶分量理论, 证明了对于具有非连通素图的有限单群, AAM猜想成立, 同时也证明了某些几乎单群也能被其非交换图刻画.上述结果推广了文献[13]的结果.In this article, we discuss the characterization of some finite （almost） simple groups by their non-commuting graphs. By using the theory of order components of finite al- most simple groups, we prove that AAM’s conjecture is true for all finite simple groups with non-connected prime graphs. Moreover, we prove that some almost simple groups can be also characterized by their non-commuting graphs. All the above results generalize those results in [13].

关 键 词：有限群 非交换图 阶分量 Thompson猜想 AAM猜想 

分 类 号：O152.1[理学—数学]