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

Authors

Reemon Spector, Hertford College, University of OxfordFollow

Abstract

In this paper we investigate actions of SAut(F_n), the unique index 2 subgroup of 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 SAut(F_n) on a set containing fewer than 20 elements is trivial.

Author Bio

Reemon is an incoming second-year undergraduate studying mathematics at the University of Oxford whose interests include group theory, probability, and programming. Outside of academia, Reemon enjoys spending time bouldering and cooking. Despite being unsure about future plans, Reemon has shown a keen interest in teaching mathematics and programming, and in pursuing further education through a PhD.

Faculty Sponsor

Professor Dawid Kielak

Recommended Citation

Spector, Reemon (2022) "On the Smallest Non-trivial Action of SAut(Fn) for Small n," Rose-Hulman Undergraduate Mathematics Journal: Vol. 23: Iss. 2, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol23/iss2/4