Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite

Nikolay Bogachev; Leone Slavich; Hongbin Sun

doi:10.1093/imrn/rnae053

Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite

Nikolay Bogachev
, Leone Slavich
, Hongbin Sun

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

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 PSO7,1 (ℝ) are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in, POn,1(ℝ),n>3, is LERF.

Original language	English (US)
Pages (from-to)	10081-10087
Number of pages	7
Journal	International Mathematics Research Notices
Volume	2024
Issue number	13
DOIs	https://doi.org/10.1093/imrn/rnae053
State	Published - Jul 1 2024

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnae053

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title = "Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite",

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 PSO7,1 (ℝ) are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in, POn,1(ℝ),n>3, is LERF.",

author = "Nikolay Bogachev and Leone Slavich and Hongbin Sun",

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N2 - A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in PSO7,1 (ℝ) are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in, POn,1(ℝ),n>3, is LERF.

AB - A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in PSO7,1 (ℝ) are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in, POn,1(ℝ),n>3, is LERF.

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Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite

Abstract

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