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Finite Contractions of Graphs with Polynomial Growth

✍ Scribed by András Lukács; Norbert Seifter

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
86 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

Let X be a locally finite, vertex-transitive, infinite graph with polynomial growth. Then there exists a quotient group of Aut(X ) which contains a finitely generated nilpotent subgroup N which has the same growth rate as X . We show that X contains a subgraph which is finitely contractible onto the h-dimensional lattice, where h is the Hirsch number of N .

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