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.

12 pages. Comments are welcome!