On the smallest non-abelian quotient of Aut(Fn)
Baumeister, Barbara
Baumeister
Barbara
Kielak, Dawid
Kielak
Dawid
Pierro, Emilio
Pierro
Emilio
We show that the smallest non-abelian quotient of Aut(Fn) is PSLn(Z/2Z)=Ln(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(Fn), the unique index 2 subgroup of Aut(Fn), can act non-trivially. We also offer new results on the representation theory of SAut(Fn) in small dimensions over small, positive characteristics and on rigidity of maps from SAut(Fn) to finite groups of Lie type and algebraic groups in characteristic 2.
118
6
1547-1591
1547-1591
Wiley
2019