Arithmetic trialitarian hyperbolic lattices are not LERF

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.

8 pages, 1 figure (minor changes like typos, etc)