Automorphisms of graph products of groups from a geometric perspective

By Anthony Genevois, Alexandre Martin. Proceedings of the London Mathematical Society, 2018

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This article studies the structure of the automorphism groups of general graph products of groups. We give a complete characterisation of the automorphisms that preserve the set of conjugacy classes of vertex groups for arbitrary graph products. Under mild conditions on the underlying graph, this allows us to provide a simple set of generators for the automorphism groups of graph products of arbitrary groups. We also obtain information about the geometry of the automorphism groups of such graph products: lack of property (T) and acylindrical hyperbolicity.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

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