The decomposable arrangement group embedding conjecture

Let ${\mathcal A}$ be a decomposable arrangement, and let $G({\mathcal A})$ denote its arrangement group. Embedding conjecture. The group $G({\mathcal A})$ embeds in a product of free groups. This would strengthen the known result that, under additional hypotheses, the quotient by the nilpotent residue is a combinatorially determined subgroup of a finite product of free groups. The conjecture is motivated by the fact that all examples considered in the paper have injective maps to products of free groups, but it is not known whether every decomposable arrangement group is residually nilpotent or admits such an embedding.