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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.16446 |
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Table of Contents:
- We study Measurable Imbeddability between groups, which is an order-like generalization of Measure Equivalence that allows the imbedded group to have an infinite measure fundamental domain. We prove if $Λ_1$ measurably imbeds into $Γ_1$, and $Λ_2$ measurably imbeds into $Γ_2$ under an additional assumption that lets the corresponding fundamental domains to be arranged in a special way, then $Λ_1 * Λ_2$ measurably imbeds into $Γ_1 * Γ_2$. Building upon the techniques we used, we show that the analogous result holds for graph products of groups.