Relative solidity for biexact groups in measure equivalence

Changying Ding; Daniel Drimbe

doi:10.48550/arxiv.2503.24167

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Relative solidity for biexact groups in measure equivalence

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Relative solidity for biexact groups in measure equivalence

Changying Ding and Daniel Drimbe

ArXiV.org

Cornell University

03/31/2025

DOI: 10.48550/arxiv.2503.24167

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We demonstrate a relative solidity property for the product of a nonamenable biexact group with an arbitrary infinite group in the measure equivalence setting. Among other applications, we obtain the following unique product decomposition for products of nonamenable biexact groups, strengthening \cite{Sa09}: for any nonamenable biexact groups Γ1,⋯,Γn, if a product group Λ1×Λ2 is measure equivalent to ×nk=1Γk, then there exists a partition T1⊔T2={1,…,n} such that Λi is measure equivalent to ×k∈TiΓk for i=1,2.

Mathematics - Group Theory

Mathematics - Operator Algebras

Details

Title: Subtitle: Relative solidity for biexact groups in measure equivalence
Creators: Changying Ding - University of California, Los Angeles
Daniel Drimbe - University of Iowa
Resource Type: Preprint
Publication Details: ArXiV.org
DOI: 10.48550/arxiv.2503.24167
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 03/31/2025
Academic Unit: Mathematics
Record Identifier: 9984805010802771

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