Profinite non-rigidity of arithmetic groups

Amir Y. Weiss Behar

doi:10.4171/GGD/815

Profinite non-rigidity of arithmetic groups

Amir Y. Weiss Behar^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

We show that for a typical higher-rank arithmetic lattice Γ, there exist finite index subgroups Γ₁ and Γ₂ such that Γ₁ 6Š Γ₂ while Γ^b₁ Š Γ^b₂. But there are exceptions to that rule.

Original language	English
Pages (from-to)	257-269
Number of pages	13
Journal	Groups, Geometry, and Dynamics
Volume	20
Issue number	1
DOIs	https://doi.org/10.4171/GGD/815
State	Published - 2026

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Publisher Copyright:
© 2024 European Mathematical Society.

Keywords

arithmetic groups
group theory
profinite rigidity

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10.4171/GGD/815

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title = "Profinite non-rigidity of arithmetic groups",

abstract = "We show that for a typical higher-rank arithmetic lattice Γ, there exist finite index subgroups Γ1 and Γ2 such that Γ1 6{\v S} Γ2 while Γb1 {\v S} Γb2. But there are exceptions to that rule.",

keywords = "arithmetic groups, group theory, profinite rigidity",

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note = "Publisher Copyright: {\textcopyright} 2024 European Mathematical Society.",

year = "2026",

doi = "10.4171/GGD/815",

language = "אנגלית",

volume = "20",

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AB - We show that for a typical higher-rank arithmetic lattice Γ, there exist finite index subgroups Γ1 and Γ2 such that Γ1 6Š Γ2 while Γb1 Š Γb2. But there are exceptions to that rule.

KW - arithmetic groups

KW - group theory

KW - profinite rigidity

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Profinite non-rigidity of arithmetic groups

Abstract

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Keywords

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