一类特殊的有限p-群

One special class of finite p-groups

探讨了一类特殊的有限p-群,即对任意x,y∈G,如果[x,y]≠1,那么〈x,y〉—G.主要证明了:如果满足这样条件的有限p-群G=〈x1,x2,…,xn〉,其中对任意x∈G,〈x〉G是交换群或者内交换群.

Let G be a finite p-group and G=〈x1,x2,…,xn〉,where｜xi=p^mi｜,i=1,2,…,n.If〈x,y〉△-G for each element x,y∈G with [x,y]≠1.Then G has order at most p^m1＋m2＋…＋mn＋n and the nilpotent class of G is at most n＋1.