7 problems

Let $G$ be the fundamental group of a $3$-manifold. A generalized torsion element is a nontrivial element whose finitely many conjugates have product equal to the identity, and $G$…

The generalized torsion criterion. In the class of 3-manifold groups, the existence of a generalized torsion element is equivalent to non-bi-orderability.

Motegi–Teragaito conjecture. If $F$ has no generalized torsion elements, then $F$ is bi-orderable.

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…

Generalized torsion conjecture. If $\pi_1(M)$ is not bi-orderable, then it contains a generalized torsion element.

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