A note on semicompleteness of graph products of abelian groups

Philip Möller; Olga Varghese

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arXiv · 2202.10083

A note on semicompleteness of graph products of abelian groups

Philip Möller·Olga Varghese

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Abstract

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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BibTeX RIS

Philip Möller, Olga Varghese. 2022-08-22. A note on semicompleteness of graph products of abelian groups. https://arxiv.org/abs/2202.10083

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