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M. Sangani Monfared
Følner's condition and expansion of Cayley graphs for group actions view print
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| Published: |
September 20, 2017 |
| Keywords: |
Invariant means, G-sets, amenable graphs, graph expansions |
| Subject: |
43A07, 58E40, 20F65 |
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Abstract
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.
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| Acknowledgements
The author was supported by an NSERC grant
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| Author information
Department of Mathematics and Statistics, University of Windsor, 401 Sunset Ave., Windsor, ON, N9B 3P4, Canada.
monfared@uwindsor.ca
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