Zassenhaus's order conjecture for torsion units in integral group rings

Let $G$ be a finite group. Write $V(\mathbb{Z}G)$ for the group of augmentation-one units of the integral group ring, and let $u\in V(\mathbb{Z}G)$ be a torsion unit.

Zassenhaus's order conjecture. There exists an element $g\in G$ such that

$$|u|=|g|.$$

This is a basic conjecture in the theory of integral group rings. The paper's abstract states that it is proved for $PSL(2,8)$ and $PSL(2,17)$, while the assertion for arbitrary finite groups remains open.