Rigidity of graph products of abelian groups

Mauricio Gutierrez*, Adam Piggott

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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 T0 property. Our results build on results by Droms, Laurence and Radcliffe.

Original languageEnglish
Pages (from-to)187-196
Number of pages10
JournalBulletin of the Australian Mathematical Society
Volume77
Issue number2
DOIs
Publication statusPublished - Apr 2008
Externally publishedYes

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