Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2009.13001 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911677647159296 |
|---|---|
| author | Hillman, J. A. |
| author_facet | Hillman, J. A. |
| contents | 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 $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_13001 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nilpotent groups with balanced presentations Hillman, J. A. Group Theory 20F18, 20J05 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 $F$. |
| title | Nilpotent groups with balanced presentations |
| topic | Group Theory 20F18, 20J05 |
| url | https://arxiv.org/abs/2009.13001 |