Rigidity of graph products of abelian groups

Details Rigidity of graph products of abelian groups Rigidity of graph products of abelian groups

2007-10-13

arxiv.org/abs/0710.2571v1

Mathematics

Group Theory

11 pages, 1 figure

Scientific paper

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.

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