Arithmetic trialitarian hyperbolic lattices are not LERF

Fuente: arXiv
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Auteurs principaux: Bogachev, Nikolay, Slavich, Leone, Sun, Hongbin
Format: Preprint
Publié: 2023
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author Bogachev, Nikolay
Slavich, Leone
Sun, Hongbin
author_facet Bogachev, Nikolay
Slavich, Leone
Sun, Hongbin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_20611
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Arithmetic trialitarian hyperbolic lattices are not LERF
Bogachev, Nikolay
Slavich, Leone
Sun, Hongbin
Group Theory
Geometric Topology
Number Theory
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.
title Arithmetic trialitarian hyperbolic lattices are not LERF
topic Group Theory
Geometric Topology
Number Theory
url https://arxiv.org/abs/2310.20611