7 problems

Periodic Šunić-group conjecture. Every periodic Šunić group belongs to $\mathcal{MF}$.

Small cancellation torsion subgroup conjecture. Every torsion subgroup of $G$ is finite.

Torsion-free CAT$(0)$ groups conjecture. There are no infinite torsion subgroups of CAT$(0)$ groups.

Let ${\mathcal G}^*_{\mathrm{met}}$ be a metric ultraproduct. A group has finite exponent, or is uniformly torsion, if there is a common positive integer annihilating every element…

A group has bounded exponent if there exists an integer $n\geq 1$ such that every element has order at most $n$. Property (T) denotes Kazhdan's property (T) for discrete groups. Sh…

Let $K$ be a division ring and let $G$ be a group. A one-sided invertible element of $K[G]$ is an element having either a left or a right inverse. The Invertibles Conjecture. If…

A finitely presented group is a group defined by finitely many generators and relations, and a torsion group is one in which every element has finite order. The corresponding quest…