On the automorphisms of a graph product of abelian groups

Abstract

We study the automorphisms of a graph product of finitely generated abelian groups W. More precisely, we study a natural subgroup Aut\* W of Aut W, with Aut\* W = Aut W whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition Aut\* W = (Inn W ⋊ Out0 W ) ⋊ Aut1 W . We also give a number of applications, some of which are geometric in nature.