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.
Cite this article
Mauricio Gutierrez, Adam Piggott, Kim Ruane, On the automorphisms of a graph product of abelian groups. Groups Geom. Dyn. 6 (2012), no. 1, pp. 125–153DOI 10.4171/GGD/153