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Arithmetic trialitarian hyperbolic lattices are not LERF (2310.20611v2)
Published 31 Oct 2023 in math.GR, math.GT, and math.NT
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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