Which finitely generated Abelian groups admit isomorphic Cayley graphs?
Group Theory
2012-08-20 v3 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1202.5484,
title = {Which finitely generated Abelian groups admit isomorphic Cayley graphs?},
author = {Clara Loeh},
journal= {arXiv preprint arXiv:1202.5484},
year = {2012}
}
Comments
16 pages; v2: added reference, reformulated quasi-convexity, v3: small corrections; to appear in Geometriae Dedicata