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19.24 (2018)

Solved

For a group $G$, let $\text{Tor}(G)$ be the normal closure of all torsion elements of $G$. Does there exist a finitely presented group $G$ such that $G/\text{Tor}(G)$ is not finitely presented? Such a group must necessarily be non-hyperbolic.

Contributor: M. Chiodo, R. Vyas

Progress

Yes, such groups exist: one soluble example and another virtually torsion-free are constructed in (I. J. Leary, A. Minasyan, J. Group Theory, 26, no. 4 (2023), 741–750).

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