辛型单群S_4(q)的纯数量刻划  

Pure Quantitative Characterization of Finite Symplectic Simple Groups S_4(q)

作　　者：许明春[1] 张林华[2] 

机构地区：[1]四川大学数学学院,四川成都610064 [2]重庆大学数理学院,重庆400044

出　　处：《重庆大学学报（自然科学版）》2002年第7期45-48,共4页Journal of Chongqing University

基　　金：国家自然科学基金 ( 198710 6 6 );教育部重点科学技术基金 ( 980 83)资助项目

摘　　要：单群的纯数量刻划在计算机识别单群方面有重大意义。而辛群从应用的角度上看也非常重要。 1989年 ,著名群论专家施武杰教授提出了单群中元的阶与群同构关系的猜想。该猜想早已作为一个公开的未解决的群论问题。对除阶大于 10 8的辛群和正交群以外的所有单群 ,该猜想已经被证明。在此基础上 ,用有限单群分类定理和素图不连通的有限群结构定理 ,并运用数论技巧 ,得到了如下定理 :设G是群 ,H =S4 (q) ,q=pn,p为素数 .则G H当且仅当 1)πe(G) =πe(H) ,2 ) ｜G｜=｜H｜。It is very important to cognize simple groups using computer by pure quantitative characterization of finite simple groups.Futhermore,finite symplectic groups are useful in many fields.In 1989, Professor Shi Wujie,a famous specialist on theory of groups put forward the conjecture about the relation between the order and the isomorphism of simple groups.The conjecture is an open problem. Until now it has been proved except for finite Symplectic and Orthogonal simple groups whose orders are more than 10 8. The authors continue the researcher and finish some important proof. By classification theorem of finite simple groups,structure theorem of finite group with disconnected prime graph and number theory techniques,the following theorem is proved: Let (G) be a finite group and H=S 4(q) be a Symplectic simple group, q=p n,where p is a prime. Then GH if and only if 1) π e(G)=π e(H); 2) |G|=|H|.

关 键 词：辛型单群 纯数量刻划 阶 元 辛群 群论 有限群 

分 类 号：O152[理学—数学]