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- W2807419191 abstract "Liouville property of actions of discrete groups can be reformulated in terms of existence co-F$o$lner sets. Since every action of amenable group is Liouville, the property can be served as an approach for proving non-amenability. The verification of this property is conceptually different than finding a non-amenable action. There are many groups that are defined by strongly transitive actions. In some cases amenability of such groups is an open problem. We define $n$-Liouville property of action to be Liouville property of point-wise action of the group on the sets of cardinality $n$. We reformulate $n$-Liouville property in terms of additive combinatorics and prove it for $n=1, 2$. The case $ngeq 3$ remains open." @default.
- W2807419191 created "2018-06-13" @default.
- W2807419191 creator A5035950080 @default.
- W2807419191 date "2018-06-07" @default.
- W2807419191 modified "2023-09-27" @default.
- W2807419191 title "A remark on Liouville property of strongly transitive actions" @default.
- W2807419191 hasPublicationYear "2018" @default.
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