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arXiv · 2009.13001

Nilpotent groups with balanced presentations

J. A. Hillman
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Abstract

We show that if a torsion free nilpotent group $G$ has a balanced presentations and Hirsch length $h(G)>3$ then $\beta_1(G;\mathbb{Q})=2$. 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 $\beta_2(G;F)=\beta_1(G;F)$ for all fields $F$.

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J. A. Hillman. 2020-09-28. Nilpotent groups with balanced presentations. https://doi.org/10.1515/jgth-2020-0169

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