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We prove that cyclic subgroup separability is preserved under exponentialcompletion for groups that belong to a class that includes all coherent RAAGsand toral relatively hyperbolic groups; we do so by exploiting the structure ofthese completions as iterated free products with commuting subgroups. From thiswe deduce that the cyclic subgroups of limit groups over coherent RAAGs areseparable, answering a question of Casals-Ruiz, Duncan and Kazachov. We alsodiscuss relations between free products with commuting subgroups and the wordproblem, and recover the fact that limit groups over coherent RAAGs and toralrelatively hyperbolic groups have a solvable word problem.

Limit groups over coherent right-angled Artin groups are cyclic subgroup separable