Uniform torsion conjecture for metric ultraproducts
Uniform torsion conjecture for metric ultraproducts
Let 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 is a torsion group, then 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.
Sources & referencesView supporting material
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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