New York Journal of Mathematics
Volume 23 (2017) 1295-1306


M. Sangani Monfared

Følner's condition and expansion of Cayley graphs for group actions

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Published: September 20, 2017
Keywords: Invariant means, G-sets, amenable graphs, graph expansions
Subject: 43A07, 58E40, 20F65

Suppose G is a group acting on a set X. If G is finitely generated and A and B are two finite symmetric generating sets, then we show that the Cayley graph CayA(G,X) is amenable if and only if CayB(G,X) is amenable. We prove that (G,X) satisfies the Følner's condition if and only if for every finitely generated subgroup H of G, Cay(H,X) is amenable. If G is finitely generated, we show that (G,X) and Cay(G,X) have the same Følner's sequences.


The author was supported by an NSERC grant

Author information

Department of Mathematics and Statistics, University of Windsor, 401 Sunset Ave., Windsor, ON, N9B 3P4, Canada.