On the Smallest Non-trivial Action of SAut(Fn) for Small n

Abstract

In this paper we investigate actions of $\mathrm{SAut}(F_n)$, the unique index $2$ subgroup of $\mathrm{Aut}(F_n)$, on small sets, improving upon results by Baumeister--Kielak--Pierro for several small values of $n$. Using a computational approach for $n⩾5$, we show that every action of $\mathrm{SAut}(F_n)$ on a set containing fewer than $18$ elements is trivial.

8 pages; typos corrected