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arXiv · 2108.13152

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

Reemon Spector
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Abstract

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

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Reemon Spector. 2021-08-30. On the Smallest Non-trivial Action of SAut(Fn) for Small n. https://arxiv.org/abs/2108.13152

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