标题： 广义扭元素和三维流形群的双序性 显示英文标题

标题： Generalized torsion elements and bi-orderability of 3-manifold groups

摘要： 已知一个双序群没有广义扭元，但反之通常不成立。 我们猜想对于三维流形的基本群，反之成立，并验证了这一猜想对于非双曲几何三维流形的情况。 我们还确认了这一猜想对于一些无限族的闭合双曲三维流形成立。 在证明过程中，我们证明了Fibonacci群F(2,m)（m>2）的每个标准生成元都是广义扭元。 显示英文摘要

摘要： It is known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of 3-manifolds, and verify the conjecture for non-hyperbolic, geometric 3-manifolds. We also confirm the conjecture for some infinite families of closed hyperbolic 3-manifolds. In the course of the proof, we prove that each standard generator of the Fibonacci group F(2,m) (m>2) is a generalized torsion element.