【摘要】 通过模仿非幂零二维李代数L₀∶[x,y]=x,构造出一个有限群族{N_n,q,b},弄清楚这些群的基本构造，并证明了对于任意的d,当n■（q-1）^d时，有限群G是非幂零的当且仅当G含有{N_n,q,b}中一个非幂零成员作为子群.更多还原

【Abstract】 By imitating the two-dimensional Lie algebra L₀:[x,y]=x which is not nilpotent, we introduce a class of finite groups {N_n,q,b}. We determine properties of these groups, and prove that a finite group G isn’t nilpotent if and only if G contains a member of {N_n,q,b} which is not nilpotent as a subgroup, when ■n（q-1）^d for any d.更多还原