5 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 $G$…

Let $M$ be a $3$-manifold and let $\pi_1(M)$ be its fundamental group. An element of a group is generalized torsion if a nonempty finite product of its conjugates is the identity;…

Let $K$ be a non-trivial knot in $S^3$, let $K(r)$ denote the $3$-manifold obtained by $r$-Dehn surgery on $K$, and let $pi_1(K(r))$ be its fundamental group. Dehn-filling generali…

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.