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A classical result of Schreier states that nontrivial finitely generatednormal subgroups of free groups are of finite index, that is, free groups canonly quotient to finite groups with finitely generated kernel.  In this note we extend this result to the class of right-angled Artin groups(RAAGs). More precisely, we prove that the quotient of a RAAG by a finitelygenerated (full) normal subgroup is abelian-by-finite and finite-by-abelian.  As Schreier's result extends to nontrivial free products of groups, wefurther show that our result extends to graph products of groups.  As a corollary, we deduce, among others, that finitely generated normalsubgroups of RAAGs have decidable word, conjugacy and membership problems andthat they are hereditarily conjugacy separable.

On finitely generated normal subgroups of right-angled Artin groups and graph products of groups