  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.
