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arXiv · 2010.03394

Metric ultraproducts of groups -- simplicity, perfectness and torsion

Jakub Gismatullin·Krzysztof Majcher·Martin Ziegler
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Abstract

We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite and infinite symmetric groups, linear groups, and interval exchange transformation groups. Using similar methods, we also examine concepts such as genericity, perfectness, and torsion.

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Jakub Gismatullin, Krzysztof Majcher, Martin Ziegler. 2024-09-27. Metric ultraproducts of groups -- simplicity, perfectness and torsion. https://doi.org/10.1016/j.jalgebra.2024.09.005

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