The automorphism group of the generalized Giulietti–Korchmáros function field

Cem Güneri; Mehmet Özdemiry; Henning Stichtenoth

doi:10.1515/advgeom-2012-0040

Published by De Gruyter March 29, 2013

The automorphism group of the generalized Giulietti–Korchmáros function field

Cem Güneri , Mehmet Özdemiry and Henning Stichtenoth

From the journal Advances in Geometry

https://doi.org/10.1515/advgeom-2012-0040

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Abstract

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 C_n 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 C_n fix the unique rational place at infinity and they are exactly the lifts of automorphisms of the Hermitian subfield H_n ⊂ C_n which fix the infinite place of H_n

Keywords: Algebraic curves; algebraic function fields; maximal curves; maximal function fields; automorphisms of function fields

The authors are supported by TÜBITAK project 111T234. The author is supported by a scholarship through the TÜBITAK project 107T897 during the writing of this manuscript.

Published Online: 2013-03-29

Published in Print: 2013-04

The automorphism group of the generalized Giulietti–Korchmáros function field

Abstract

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