论文标题
某些无扭转的可溶解组，很少
Some torsion-free solvable groups with few subquotients
论文作者
论文摘要
我们构建了有限生成的无扭转的可解决方案$ g $，这些$ g $具有无限的排名，但所有有限生成的无扭转的metabelian subsecortiations $ g $的亚果实实际上都是Abelian。特别是所有有限生成的$ G $的Metabelian子组几乎都是Abelian。此类组的存在表明，P。Kropholler的定理没有“无扭转版本”，该定理通过其Metabelian亚贵族来表征可解决的无限等级组。
We construct finitely generated torsion-free solvable groups $G$ that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of $G$ are virtually abelian. In particular all finitely generated metabelian subgroups of $G$ are virtually abelian. The existence of such groups shows that there is no "torsion-free version" of P. Kropholler's theorem, which characterises solvable groups of infinite rank via their metabelian subquotients.
