p~2q~2阶群的完全分类

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q~2(×)p~2矿-1时,恰有4个彼此不同构的类型;当q∣ p-1但q~2(×)p~2矿-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~2(×)p+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.

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

Let p, q be odd primes such that p＞q, let G be a finite group of order p~2q~2. This paper discusses that the isomorphic classification of G, and their presentations are completely described. It showes that: If q(×)p~2 - 1, G has 4 nonisomorphic presentations; If q∣p- 1 and q~2(×)p-1, G has 11 nonisomorphic presentations; If q~2∣p-1, G has 15 nonisomorphic presentations; If q∣p+1 and q~2(×)p+1, G has 6 nonisomorphic presentations; If q~2 ∣p+1, G has 7 nonisomorphic presentations.