TY - JOUR
T1 - Rigidity of graph products of abelian groups
AU - Gutierrez, Mauricio
AU - Piggott, Adam
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
KW - Graph products of groups
UR - http://www.scopus.com/inward/record.url?scp=44949130636&partnerID=8YFLogxK
U2 - 10.1017/S0004972708000105
DO - 10.1017/S0004972708000105
M3 - Article
SN - 0004-9727
VL - 77
SP - 187
EP - 196
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 2
ER -