4 problems

Let $G$ be the fundamental group of a $3$-manifold. A non-trivial element $g\in G$ is a generalized torsion element if some non-empty finite product of conjugates of $g$ equals the…

Let $G$ be the fundamental group of a $3$--manifold. A generalized torsion element is a non-trivial element whose non-empty finite product of conjugates is the identity, and $G$ is…

Bi-orderability conjecture. $G$ is bi-orderable if and only if $G$ has no generalized torsion element.

Generalized-torsion conjecture. $G$ is bi-orderable if and only if $G$ has no generalized torsion element.