Arithmetic trialitarian hyperbolic lattices are not LERF
arXiv (Cornell University)(2023)
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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Key words
arithmetic trialitarian hyperbolic lattices
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