Direct products of coprime-order CI-groups

Prove or disprove that the direct product of two CI-groups of coprime orders is a CI-group.

Background

The CI-property asks whether every isomorphism between Cayley digraphs or graphs over a fixed group can be realized by a group automorphism. The paper recalls a conjecture that this property is preserved under direct products of CI-groups whose orders are coprime. Theorem 1.1 proves an analogous closure statement for abelian NCI(2)-groups, but it does not resolve the broader CI-group conjecture.