特征为2的特殊射影酉群的谱刻画  

Recognition by spectrum for finite projective special unitary groups over fields of characteristic 2

作　　者：何怀玉[1] 

机构地区：[1]上海政法学院经济管理学院,上海201701

出　　处：《辽宁工程技术大学学报（自然科学版）》2016年第5期552-556,共5页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金青年科学基金项目(11201401);上海市优青基金项目(szf10016);上海政法学院青年科研基金项目(2014XQN22)

摘　　要：为解决素图非连通的特殊射影酉群2^An（2）的数量刻画问题,根据单群的分类,先后探讨了各系列单群的连通情况,确定了其中的元素的阶的集合和全连通的素图分支,揭示了李型单群的Frobenius子群的结构,结合素数方程的解的情况,采取排除法,逐步证实了谱和2^An（2）一样的有限群均与2^An（2）同构,仅2^A4（2）除外.研究结果表明：Kondratiev的猜想对于2^An（2）是成立的,从而推进了该猜想的解决,同时可以看到,类似于An（q）的刻画工作也可以移植到2An（q）上,有助于其他2^An（q）型单群的刻画.For finite projective special unitary groups over fields of characteristic 2 with disconnected prime graph, in order to solve its characterization by quantitative properties, this paper investigated the adjacency criterions of a series of simple groups, and ascertained the set of element orders and the connected component of prime graph, then disclosed the Frobenius- subgroups of simple groups of Lie type. With the solutions of Diophantine equations, 2^An（2） was recognized by the set of element orders, in which the classification of finite simple groups and elimination are employed. Above study prove that Kondartiev＇s conjecture is true to simple groups 2^An（2） except 2^A4（2）, which promotes the further solution of this conjecture. At the same time, the same work on An（q） can also be applied to 2^An（2）, which will be helpful for the recognition of the rest of finite simple groups 2^An（q）.

关 键 词：谱 素图 刻画 猜想 非连通图 

分 类 号：O152.1[理学—数学]