Geodesic
Homogeneous actions on the random graph
Pierre Fima1 ; Soyoung Moon2 ; Yves Stalder3
1Université de Paris, Sorbonne Université, France
2Université de Bourgogne, Dijon, France
3Université Clermont Auvergne, Clermont-Ferrand, and Université Blaise Pascal, Aubière, France
Groups, geometry, and dynamics, Tome 15 (2021) no. 1, pp. 1-34

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DOI

We show that any free product of two (non-trivial) countable groups, one of them being infinite, admits a faithful and homogeneous action on the random graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the random graph whose action on it have all orbits infinite.
DOI : 10.4171/ggd/589
Classification : 20-XX, 05-XX, 54-XX
Mots-clés : Homogeneous actions, random graph, free groups, groups acting on trees, Baire category theorem

Pierre Fima  1   ; Soyoung Moon  2   ; Yves Stalder  3

1 Université de Paris, Sorbonne Université, France
2 Université de Bourgogne, Dijon, France
3 Université Clermont Auvergne, Clermont-Ferrand, and Université Blaise Pascal, Aubière, France 
Pierre Fima; Soyoung Moon; Yves Stalder. Homogeneous actions on the random graph. Groups, geometry, and dynamics, Tome 15 (2021) no. 1, pp. 1-34. doi: 10.4171/ggd/589
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