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arXiv · 2310.20611

Arithmetic trialitarian hyperbolic lattices are not LERF

Nikolay Bogachev·Leone Slavich·Hongbin Sun
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Abstract

A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that all arithmetic lattices in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, are not LERF.

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Nikolay Bogachev, Leone Slavich, Hongbin Sun. 2023-10-31. Arithmetic trialitarian hyperbolic lattices are not LERF. https://arxiv.org/abs/2310.20611

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