Ottilia Andersson: Outer automorphisms of S6

Abstract

In this thesis, we study inner and outer automorphisms of groups, with a particular focus on the symmetric group. We show that if an automorphism of S_n stabilizes the conjugacy class of transpositions, then it is inner. Using this result, we further show that every automorphism of S_n is inner if \(n\neq 6\). Finally, a proof of the existence of an outer automorphism of S₆ is outlined.