关于幂零群的特征

ON THE CMARACTERIZATION OF NILPOTENT GROUPS

有限幂零群的特征性质在[1]、[2]中已给出了许多,本文通过次中心给出了幂零群的两个充要条件。其一,G=SZ(G),SZ(G)是G的超次中心;其二,G幂零的充要条件是G/SZ(G)是幂零的。本文限定都是有限群。

The main results of this paper are:Theorem2: the group G is nilpotent if and only if G = SZ*(G), SZ* ( G ) is hypersubcenter of GTheorem 5 the group G is nilpotent if and only if G/SZ* ( G ) is nilpotent.