Abstract
The group F was invented in the 1960s by Richard Thompson, and is a subgroup of the group of all piecewise linear, orientation preserving homeomorphisms of the unit interval. R. Geoghegan has conjectured that F is an example of a finitely presented nonamenable group which has no free subgroup on two generators. In this article, we study properties of F related to amenability. We state some necessary conditions that a sequence of nonempty finite subsets of F must satisfy to be a sequence of Folner sets of F.
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