论文标题
具有平衡演示文稿的尼尔植物群体
Nilpotent groups with balanced presentations
论文作者
论文摘要
我们表明，如果免费的nilpotent grout $ g $具有平衡的演示文稿，并且hirsch Length $ h（g）> 3 $，则$β_1（g; \ mathbb {q}）= 2 $。只有一个这样的组无扭转和赫希长度$ h = 4 $，而没有$ h = 5 $。我们还用$ h = 6 $构建了一个无扭转的nilpotent $ g $，并且所有字段$ f $ $β_2（g; f）=β_1（g; f）$。
We show that if a torsion free nilpotent group $G$ has a balanced presentations and Hirsch length $h(G)>3$ then $β_1(G;\mathbb{Q})=2$. There is just one such group which is torsion-free and of Hirsch length $h=4$, and none with $h=5$. We also construct a torsion-free nilpotent group $G$ with $h=6$ and such that $β_2(G;F)=β_1(G;F)$ for all fields $F$.
