A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in PSO_{7,1}(R) are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in PO_{n,1}(R), n > 3, is LERF.
Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite
Slavich, Leone;
2024-01-01
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 PSO_{7,1}(R) are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in PO_{n,1}(R), n > 3, is LERF.File in questo prodotto:
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