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arXiv · 2102.02947

Elementary amenable groups of cohomological dimension 3

Jonathan A. Hillman
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Abstract

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 $\pi_1(Kb)$.

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Jonathan A. Hillman. 2021-02-05. Elementary amenable groups of cohomological dimension 3. https://doi.org/10.1515/jgth-2022-0049

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