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Mathematics > Group Theory
Title: Measurable Imbeddings, Free Products, and Graph Products
(Submitted on 29 Oct 2022 (v1), last revised 28 Mar 2024 (this version, v2))
Abstract: 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 $\Lambda_1$ measurably imbeds into $\Gamma_1$, and $\Lambda_2$ measurably imbeds into $\Gamma_2$ under an additional assumption that lets the corresponding fundamental domains to be arranged in a special way, then $\Lambda_1 * \Lambda_2$ measurably imbeds into $\Gamma_1 * \Gamma_2$. Building upon the techniques we used, we show that the analogous result holds for graph products of groups.
Submission history
From: Özkan Demir [view email][v1] Sat, 29 Oct 2022 00:06:10 GMT (8kb)
[v2] Thu, 28 Mar 2024 03:04:49 GMT (14kb)
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