A note on semicompleteness of graph products of abelian groups

In this short note we prove that a graph product $G_Γ$ of finitely generated abelian groups is semicomplete -- that is the kernel of the natural homomorphism ${\rm Aut}(G_Γ)\to{\rm Aut}(G_Γ^{ab})$ induced by the abelianization of $G_Γ$ is equal to the inner automorphisms -- if and only if $Γ$ does not have a separating star.

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