有限群的某些数量关系

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G1auberman正规p-补定理分别对两类阶具有3个素因子的群：p^2qr和p^3qr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)．

Some Scalar Relationship of Finite Group

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.