Which finitely generated Abelian groups admit isomorphic Cayley graphs?

Details Which finitely generated Abelian groups admit isomorphic Cayley graphs? Which finitely generated Abelian groups admit isomorphic Cayley graphs?

2012-02-24

arxiv.org/abs/1202.5484v2

Mathematics

Group Theory

15 pages; v2: added reference, reformulated quasi-convexity

Scientific paper

We show that Cayley graphs of finitely generated Abelian groups are rather
rigid. As a consequence we obtain that two finitely generated Abelian groups
admit isomorphic Cayley graphs if and only if they have the same rank and their
torsion parts have the same cardinality. The proof uses only elementary
arguments and is formulated in a geometric language.

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