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RIGIDITY OF GRAPH PRODUCTS OF ABELIAN GROUPS
Published online by Cambridge University Press: 01 April 2008
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.
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- Research Article
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- Copyright © 2008 Australian Mathematical Society
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