We study hereditary properties of the class of countable groups admitting an amenable, transitive and faithful action on a countable set. We consider mainly the case of amalgamated free products, and we show in particular that the double of amenable groups and the amalgamated free products of two amenable groups over a finite subgroup admit such actions.
"Permanence properties of amenable, transitive and faithful actions." Bull. Belg. Math. Soc. Simon Stevin 18 (2) 287 - 296, may 2011. https://doi.org/10.36045/bbms/1307452078