k-N群的局部定义方式

k-N GROUP AND ITS LOCAL DEFINITION

我们称群G为k-N群,如果G的第k次导群G^(k)是幂零群。我们证明了所有的有限k-N群的全体构成一个饱和群系,并证明了{F(p)}是局部定义k-N群的完整且集中的群系组,其中每个F(p)={L|L^(k)∈P},进一步得出了k-N群的一些性质与判别方法。

A group G is called k-N group if G(k) is nilpotent. It is proved that all k-N groups form a saturated formation and that the unique full and integrated local definition way of k-N group is {F(p)}, where F(p) = {L| L(k)∈P}. As a result, some criterions on k-N group have been obtained.