有限群的某些数量关系  

Some Scalar Relationship of Finite Group

作　　者：徐荣华[1] 赵可琴[1] 

机构地区：[1]郑州大学数学系,郑州450052

出　　处：《郑州大学学报（理学版）》2003年第2期16-18,22,共4页Journal of Zhengzhou University:Natural Science Edition

摘　　要：在有限单群分类过程中 ,其阶恰包含 3个素因子的群 ,即所谓K3 群构成了一类需要单独进行处理的单群类 .利用Sylow定理和Glauberman正规p 补定理分别对两类阶具有 3个素因子的群 :p2 qr和p3qr阶群进行了讨论 ,在一定条件下证明了它们都是非可换单群 ,即K3 群 ,并且分别同构于A5和L( 2 ,7)In the course of the classification of the finite simple groups, the K 3-group which contains three prime factors constitutes a kind of simple groups.It is needed to study individually.Using Sylow Theorem and Glauberman Normal p-Complement Theorem,the groups of order p 2qr and p 3qr are studied respectively;It is proved that under certain conditions both of them are non-abelian simple groups,i.e. K 3-group.Moreover,they are isomorphic to A 5 and L(2,7) respectively.

关 键 词：有限群 数量关系 素因子 单群 SYLOW定理 G1auberman正规p-补定理 同构 

分 类 号：O152.1[理学—数学]