群的几个幂零性条件

On Some Nilpotency Criteria for Groups

如果G的所有子群都是次正规的,而且G满足下面条件之一,那么G是幂零群.(1)G有一个次正规列1△H△K△G,其中K/H是幂零群,H和G/K是有限生成的;(2)G有一个正规子群N使得,N在其子集的中心化子上满足极小条件,并且G/N是有限生成的.

If all subgroups of G are subnormal,then G is nilpotent if it satisfies one of the following conditions： （1） G has a subnormal series 1△ H△ K△ G,in which factor K/H is nilpotent,H and G/K are finitely generated; （2） G has a normal subgroup N such that N satisfies the minimal condition on centralizers and G/N is finitely generated.