Finitely presented infinite torsion groups

Determine whether finitely presented infinite torsion groups exist.

Background

The paper relates its fixed-point conjectures to broader questions concerning the structure of infinite torsion groups. In particular, the existence of finitely presented infinite torsion groups is presented as a fundamental unresolved problem.

This question is relevant because the paper studies actions of finitely generated torsion groups on nonpositively curved complexes and seeks to constrain when such groups can act without global fixed points.

References

In particular, (not only) we believe (cf. e.g. ) this is related to the following fundamental question about torsion groups: Are there finitely presented infinite torsion groups?

— Locally elliptic actions, torsion groups, and nonpositively curved spaces  (2110.12431 - Haettel et al., 2021) in Section 2, Subsection 2.2, item (IX)