Different subsets F of {2,3,...} give groups G_F whose von Neumann algebras are not W*-correlated, hence not measure equivalent nor W*-equivalent.
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W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
Different subsets F of {2,3,...} give groups G_F whose von Neumann algebras are not W*-correlated, hence not measure equivalent nor W*-equivalent.