Rigidity of graph products of abelian groups

Abstract

We show that if $G$ is a group and $G$ has a graph-product decomposition with finitely-generated abelian vertex groups, then $G$ has two canonical decompositions as a graph product of groups: a unique decomposition in which each vertex group is a directly-indecomposable cyclic group, and a unique decomposition in which each vertex group is a finitely-generated abelian group and the graph satisfies the $T_0$ property. Our results build on results by Droms, Laurence and Radcliffe.

11 pages, 1 figure

References in corpus (1)

• Rigidity of graph products of groups

Cited by in corpus (3)

• Geometry of right-angled Coxeter groups on the Croke-Kleiner spaces
• The automorphism group of a graph product with no SIL
• Actions of Right-Angled Coxeter Groups on the Croke Kleiner Spaces