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arXiv · 2410.10152

On residual finiteness of graphs of free groups with cyclic edge groups

Adrien Abgrall·Zachary Munro
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Abstract

We characterize which groups splitting as finite graphs of free groups with cyclic edge groups are residually finite. Such a group $G$ is residually finite if and only if all its Baumslag-Solitar subgroups are residually finite. From a presentation of $G$, we construct a finite labeled graph $\Gamma$, and show that residual finiteness of $G$ is equivalent to an easily-detectable property of this graph. This characterization proves a conjecture of Wise.

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Adrien Abgrall, Zachary Munro. 2024-10-14. On residual finiteness of graphs of free groups with cyclic edge groups. https://arxiv.org/abs/2410.10152

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