p^2q^2阶群的完全分类

On the classification of finite groups of order p^2q^2

设p,q为奇素数,且p>q,本文对p^2q^2阶群进行了完全分类并获得了其全部构造:当qp^2-1时,恰有4个彼此不同构的类型;当q|p-1但q^2p-1时,恰有11个彼此不同构的类型;当q^2|p-1时,恰有15个彼此不同构的类型;当q|p+1但q^2p+1时,恰有6个彼此不同构的类型;当q^2|p+1时,恰有7个彼此不同构的类型.

Let p, q be odd primes such that p〉q, This paper discusses that the isomorphic classifica completely described. It showes that ： If q p^2 - 1, If q｜p-1 and q^2 p-1, G has 11 nonisomorphic let G be a finite group of order p^2q^2. tion of G, and their presentations are G has 4 nonisomorphic presentations; presentations; If q^2｜ p-1, G has 15 nonisomorphic presentations; If q｜ p＋1 and q^2 p＋1, G has 6 nonisomorphic presenta tions; If q^2｜ p＋1, G has 7 nonisomorphic presentations.