The Giulietti-Korchmáros (GK) function field is the first example of a maximal function field which is not a subfield of the Hermitian function field over the same constant field. The generalized GK function field Cn was later introduced by Garcia, Güneri and Stichtenoth and was shown to be maximal too. In the present article we determine the automorphism group of the generalized GK function field. We prove that all the automorphisms of Cn fix the unique rational place at infinity and they are exactly the lifts of automorphisms of the Hermitian subfield Hn ⊂ Cn which fix the infinite place of Hn

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Abstract. In this article, we show that many of the genera that Giulietti and Fanali obtained from subfields of the GK curve can be obtained by using similar techniques used by Garcia, Stichtenoth and Xing. In the meantime, we obtain some new genera from the subfields of GK and generalized GK function fields.

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