Highly Transitive Actions of Out(Fn)

Abstract

An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n>3 the group Out(Fn) = Aut(Fn)/Inn(Fn) admits a faithful highly transitive action on a countable set.

14 pages, (minor corrections to match final published version)

References in corpus (4)

• Dynamics of Aut(Fn) Actions on Group Presentations and Representations
• Compactifications and algebraic completions of Limit groups
• On the utility of Robinson-Amitsur ultrafilters. II
• Highly Transitive Actions of Surface Groups

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• Generic IRS in free groups, after Bowen
• Measure equivalence rigidity of $\mathrm{Out}(F_N)$
• Highly transitive actions of groups acting on trees
• On quasi-2-transitive actions of branch groups