JournalsggdVol. 15, No. 1pp. 1–34

Homogeneous actions on the random graph

  • Pierre Fima

    Université de Paris, Sorbonne Université, France
  • Soyoung Moon

    Université de Bourgogne, Dijon, France
  • Yves Stalder

    Université Clermont Auvergne, Clermont-Ferrand, and Université Blaise Pascal, Aubière, France
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Abstract

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.

Cite this article

Pierre Fima, Soyoung Moon, Yves Stalder, Homogeneous actions on the random graph. Groups Geom. Dyn. 15 (2021), no. 1, pp. 1–34

DOI 10.4171/GGD/589