摘要
如果对多重循环群Ｇ的每个有限剩余的真子群都是可以由二元生成的，那么我们就把Ｇ叫做ＲＤ＿２－群。在本文里，我们确定了无限的ＲＤ＿２－群的结构，证明了ＲＤ＿２－群是可以由二元生成的。这些结果推广了作者已经得到的关于无限的可解ＳＤ＿２群的全部结果，见［４］．
Let G be a polycyclic group of infinite order. we show that G is 2-generated andof Hirsch length 1 or 2 if every proper subgroup of arbitrary finite quotient group of G is 2-0generated.If it is the case,moreover, G is both supersolvable and metabelian if its Hirsch lengthis1, and G(3)= 1 and G is a natural extension of by certain finite subgroup of GL(2,Z)if its Hirb,ch length is 2.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1994年第6期721-727,共7页
Acta Mathematica Sinica：Chinese Series
关键词
生成元
RD2群
可解群
有限剩余
polycyclic group,Hirsch length,2generated,finite residue
