Highly transitive actions of Out(Fn)\operatorname{Out}(F_n)

  • Shelly Garion

    Universität Münster, Germany
  • Yair Glasner

    Ben Gurion University of the Negev, Beer Sheva, Israel


An action of a group on a set is called kk-transitive if it is transitive on ordered kk-tuples and highly transitive if it is kk-transitive for every kk. We show that for n4n \ge 4 the group Out(Fn)=Aut(Fn)/Inn(Fn)\operatorname{Out}(F_n) = \operatorname{Aut}(F_n) / \mathrm{Inn}(F_n) admits a faithful highly transitive action on a countable set.

Cite this article

Shelly Garion, Yair Glasner, Highly transitive actions of Out(Fn)\operatorname{Out}(F_n). Groups Geom. Dyn. 7 (2013), no. 2, pp. 357–376

DOI 10.4171/GGD/185