Groups, Geometry, and Dynamics

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Volume 6, Issue 1, 2012, pp. 125–153
DOI: 10.4171/GGD/153

Published online: 2012-02-08

On the automorphisms of a graph product of abelian groups

Mauricio Gutierrez[1], Adam Piggott[2] and Kim Ruane[3]

(1) Tufts University, Medford, USA
(2) Bucknell University, Lewisburg, USA
(3) Tufts University, Medford, USA

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 ⋊ Out0W ) ⋊ Aut1W . We also give a number of applications, some of which are geometric in nature.

Keywords: Automorphism groups, graph products of groups, right-angled Coxeter groups, right-angled Artin groups

Gutierrez Mauricio, Piggott Adam, Ruane Kim: On the automorphisms of a graph product of abelian groups. Groups Geom. Dyn. 6 (2012), 125-153. doi: 10.4171/GGD/153