Bi-orderability and generalized torsion elements from the perspective of profinite properties
Abstract
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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