The conjecture that every torsionfree group is a Linnell group

A Linnell group is a group for which, for every field $F$ and crossed product $F\ast G$, a Linnell division ring $\iota\colon F\ast G\to\mathcal D_{F\ast G}$ exists and is unique up to $F\ast G$-isomorphism. Torsionfree-groups conjecture. Every torsionfree group is a Linnell group.

This conjecture concerns the existence and uniqueness of division-ring embeddings for group crossed products. The source attributes it to Jaikin-Zapirain; its status is not resolved in the supplied text.