The conjecture that locally indicable groups are Lewin groups

A group $G$ is a Lewin group if, for every field $F$ with a $G$-action, the crossed product $F\ast G$ admits a Hughes-free $F\ast G$-division ring that is its universal division ring of fractions. Locally indicable groups conjecture. Every locally indicable group is a Lewin group, and in particular a Hughes group.

The conjecture links local indicability with the universal division-ring-of-fractions property. The source attributes it to Jaikin-Zapirain; its status is not resolved in the supplied text.