This research demonstrates bi-orderability's lack of profinite properties in certain groups, suggesting new insights in group theory.
Using fiber products, we construct bi‐orderable groups from left‐orderable groups. As an application, we show that bi‐orderability is not a profinite property, answering a question of Piwek and Wykowski negatively. We also show that the existence of a generalized torsion element is not a profinite property.
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Jang et al. (2026) studied this question.
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