Elementary amenable groups of cohomological dimension 3
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909038522925056 |
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| author | Hillman, Jonathan A. |
| author_facet | Hillman, Jonathan A. |
| contents | We show that torsion-free elementary amenable groups of Hirsch length $\leq3$ are solvable, of derived length $\leq3$. This class includes all solvable groups of cohomological dimension 3. We show also that groups in the latter subclass are either polycyclic, semidirect products $BS(1,n)\rtimes\mathbb{Z}$ or properly ascending HNN extensions with base $\mathbb{Z}^2$ or $π_1(Kb)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_02947 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Elementary amenable groups of cohomological dimension 3 Hillman, Jonathan A. Group Theory 20F16, 20J06 We show that torsion-free elementary amenable groups of Hirsch length $\leq3$ are solvable, of derived length $\leq3$. This class includes all solvable groups of cohomological dimension 3. We show also that groups in the latter subclass are either polycyclic, semidirect products $BS(1,n)\rtimes\mathbb{Z}$ or properly ascending HNN extensions with base $\mathbb{Z}^2$ or $π_1(Kb)$. |
| title | Elementary amenable groups of cohomological dimension 3 |
| topic | Group Theory 20F16, 20J06 |
| url | https://arxiv.org/abs/2102.02947 |