The class S as an ME invariant

TL;DR

This paper proves that membership in Ozawa's class S is preserved under measure equivalence, establishing it as an invariant in the study of measure equivalence of groups.

Contribution

It introduces the result that Ozawa's class S is a measure equivalence invariant, expanding understanding of invariants in group theory.

Findings

Class S is a measure equivalence invariant

Provides new tools for analyzing measure equivalence

Enhances classification of groups based on invariants

Abstract

We prove that being in Ozawa's class $\mathcal{S}$ is a measure equivalence invariant.