Abstract: The groups,in which the number of prime divisors in the order is small and the degrees of each prime divisor in the order are small too,have important significance in the research of groups.Many results of structure of groups,such as the structure of solvable groups,are narrated by using these groups.Using the method of linear group and the ideals of linear representation of group,a sufficient condition that two relative holomorphs of Z_p×Z_p are isomorphic is given.By using it,another proof of the number of groups of order p²q is given,which is non-isomorphic groups pair-wisely.

Key words: finite group, isomorphism, action, holomorph

摘要： 阶素因子个数较小且每个素因子的次数较低的有限群在群的研究中有重要的作用,很多与群结构相关的结论都是利用这种群描述的(比如可解群)。利用线性群的方法以及群的线性表示的思想,给出Z_p×Z_p的两个相对全形同构的一个性质充分条件,并利用这一充分条件,给出p²q阶群的同构类数的另一证明。

关键词: 有限群, 同构, 群作用, 全形