On the smallest non‐abelian quotient of Aut(Fn) - Baumeister, B; Kielak, D; Pierro, E (Wiley, 2019)
We show that the smallest non-abelian quotient of $Aut(F_n)$ is $PSL_n(\mathbb{Z}/2\mathbb{Z}) = L_n(2)$, thus confirming a conjecture of Mecchia--Zimmermann. In the course of the proof we give an exponential (in $n$) lower bound for the cardinality of a set on which $SAut(F_n)$, the unique index $2$ subgroup of $Aut(F_n)$, can act non-trivially. We also offer new results on the representation theory of $SAut(F_n)$ in small dimensions over small, positive characteristics, and on rigidity of maps from $SAut(F_n)$ to finite groups of Lie type and algebraic groups in characteristic $2$.