The automorphism group of the generalized Giulietti-Korchmaros function field

Abstract

The Giulietti-Korchmaros (GK) function eld is the rst example of a maximal function eld which is not a subeld of the Hermitian function eld over the same constant eld. The generalized GK function eld Cn was later introduced by Garcia, Guneri and Stichtenoth and was shown to be maximal too. In the present article we determine the automorphism group of the generalized GK function eld. We prove that all the automorphisms of Cn x the unique rational place at innity and they are exactly the lifts of automorphisms of the Hermitian subeld Hn Cn which x the innite place of Hn.