Groups, Geometry, and Dynamics

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Volume 7, Issue 2, 2013, pp. 357–376
DOI: 10.4171/GGD/185

Published online: 2013-05-07

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

Shelly Garion[1] and Yair Glasner[2]

(1) Universit√§t M√ľnster, Germany
(2) Ben Gurion University of the Negev, Beer Sheva, Israel

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

Keywords: Highly transitive action, outer automorphism group, free group

Garion Shelly, Glasner Yair: Highly transitive actions of $\operatorname{Out}(F_n)$. Groups Geom. Dyn. 7 (2013), 357-376. doi: 10.4171/GGD/185