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

Shelly Garion; Yair Glasner

doi:10.4171/ggd/185

JournalsggdVol. 7, No. 2pp. 357–376

Highly transitive actions of $Out (F_{n})$

Shelly Garion
Universität Münster, Germany
Yair Glasner
Ben Gurion University of the Negev, Beer Sheva, Israel

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

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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 $n \geq 4$ the group $Out (F_{n}) = Aut (F_{n}) / Inn (F_{n})$ admits a faithful highly transitive action on a countable set.

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Shelly Garion, Yair Glasner, Highly transitive actions of $Out (F_{n})$ . Groups Geom. Dyn. 7 (2013), no. 2, pp. 357–376

DOI 10.4171/GGD/185