A generating set for the automorphism group of a graph product of abelian groups

TL;DR

This paper identifies a generating set for the automorphism group of a graph product of finitely generated abelian groups using a labeled graph, and also provides generators for a key subgroup of star-automorphisms, following Laurence's approach.

Contribution

It introduces a method to derive generators for the automorphism group of such graph products directly from the associated labeled graph, extending previous work on star-automorphisms.

Findings

Generated the automorphism group from the labeled graph

Provided generators for the star-automorphisms subgroup

Followed Laurence's plan for the proof

Abstract

We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined in [7]. We follow closely the plan of M. Laurence's paper [11].