Commensurability growths of algebraic groups

Khalid Bou-Rabee; Tasho Kaletha; Daniel Studenmund

doi:10.1007/s00209-019-02334-5

Commensurability growths of algebraic groups

Khalid Bou-Rabee
, Tasho Kaletha
, Daniel Studenmund

Mathematics and Statistics

Binghamton University

City University of New York
University of Michigan, Ann Arbor

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

Abstract

Fixing a subgroup Γ in a group G, the full commensurability growth function assigns to each n the cardinality of the set of subgroups Δ of G with [Γ: Γ∩ Δ] [Δ: Γ∩ Δ] ≤ n. For pairs Γ≤ G, where G is a higher rank Chevalley group scheme defined over Z and Γ is an arithmetic lattice in G, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on G.

Original language	English
Pages (from-to)	1749-1757
Number of pages	9
Journal	Mathematische Zeitschrift
Volume	294
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-019-02334-5
State	Published - Apr 1 2020

Keywords

Algebraic groups
Commensurators
Residually Finite groups

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10.1007/s00209-019-02334-5

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AU - Studenmund, Daniel

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N2 - Fixing a subgroup Γ in a group G, the full commensurability growth function assigns to each n the cardinality of the set of subgroups Δ of G with [Γ: Γ∩ Δ] [Δ: Γ∩ Δ] ≤ n. For pairs Γ≤ G, where G is a higher rank Chevalley group scheme defined over Z and Γ is an arithmetic lattice in G, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on G.

AB - Fixing a subgroup Γ in a group G, the full commensurability growth function assigns to each n the cardinality of the set of subgroups Δ of G with [Γ: Γ∩ Δ] [Δ: Γ∩ Δ] ≤ n. For pairs Γ≤ G, where G is a higher rank Chevalley group scheme defined over Z and Γ is an arithmetic lattice in G, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on G.

KW - Algebraic groups

KW - Commensurators

KW - Residually Finite groups

UR - https://www.scopus.com/pages/publications/85066054016

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Commensurability growths of algebraic groups

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