Displaying similar documents to “Sur les ensembles denses de puissance minimum dans les groupes topologiques”

Testing Cayley graph densities

Goulnara N. Arzhantseva, Victor S. Guba, Martin Lustig, Jean-Philippe Préaux (2008)

Annales mathématiques Blaise Pascal

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We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m -generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2 m . We test amenable and...