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arXiv · 2209.04085

Structure of Cross-wired Lamplighter Groups

Benjamin L. Jeffers
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Abstract

We answer a question posed by Cornulier, Fisher, and Kashyap, proving that for a closed cocompact subgroup $\Gamma$ of $\text{Isom}(\text{DL}(n, n))$ not contained in $\text{Isom}^+(\text{DL}(n, n))$, the sequence $1 \to H \to \Gamma \to D_\infty \to 1$ splits, where $H$ is the unique open normal subgroup such that $\Gamma/H \cong D_\infty$.

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Benjamin L. Jeffers. 2022-09-09. Structure of Cross-wired Lamplighter Groups. https://arxiv.org/abs/2209.04085

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