Orderable group

Summary

An orderable group, or bi-orderable group, is a group that admits a total order preserved by multiplication on both sides. In other words, it is a group that can be made into a linearly ordered group. Orderability is a property of the group, not extra structure, and a group can have many different orders. Torsion-free abelian groups and free groups are orderable, while groups with nontrivial elements of finite order are not.