满足某些条件的有限单群的分类  

The Classification of Finite Simple Groups with Some Conditions

作　　者：王玲丽[1] 张良才[2] WANG Ling-li;ZHANG Liang-cai(School of Science, North University of China, Taiyuan 030051, China;College of Mathematics and Statistics, Chongqing Unviersity, Chongqing 401331, China)

机构地区：[1]中北大学理学院,山西太原030051 [2]重庆大学数学与统计学院,重庆401331

出　　处：《中北大学学报（自然科学版）》2019年第4期308-312,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271301,11471266);国家青年科学基金资助项目(11401324);教育部第47批留学回国人员科研启动基金资助项目

摘　　要：进一步探讨了有限非交换单群的素图,考虑了顶点度数对其结构的影响,利用数论知识,素图完全图的分类,以及有限非交换单群的素图连接标准,得到了群阶不超过1010的素图每个分支为完全图且7∈π(G),dG(7)=1的有限非交换单群的分类.该分类问题进一步完善了有限单群的素图信息,借助此方法,还可以解决群阶包含其他素数的有限非交换单群的分类.The prime graph of the finite nonabelain simple group was investigated in further and the influence of vertex degrees on the structure was considered. Using the number theory, the classification of complete prime graph and the adjacency criterion for the prime graph of the finite nonabelain simple groups, the classification of the finite nonabelain simple group G with complete prime graph components satisfying | G |<10 10 , 7∈π( G ) and d G (7)=1 is given. The problem further completed the information of prime graph. And using this method, the classification of the finite nonabelain simple group with the other prime can also be solved.

关 键 词：素图 单群 完全图 顶点度数 

分 类 号：O152.1[理学—数学]