Uniform torsion conjecture for metric ultraproducts

Let Gmet{\mathcal G}^*_{\mathrm{met}} be a metric ultraproduct. A group has finite exponent, or is uniformly torsion, if there is a common positive integer annihilating every element. The uniform torsion conjecture. If Gmet{\mathcal G}^*_{\mathrm{met}} is a torsion group, then Gmet{\mathcal G}^*_{\mathrm{met}} has finite exponent. For ordinary ultraproducts, torsion is known to be equivalent to uniform torsion; the conjecture asks whether the same equivalence holds for every metric ultraproduct.

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Primary source

Jakub Gismatullin, Krzysztof Majcher and Martin Ziegler, “Metric ultraproducts of groups – simplicity, perfectness and torsion”, arXiv:2010.03394 (2024).

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