# IJPAM: Volume 78, No. 7 (2012)

GALOIS GROUPS OF FUNCTION FIELDS
WITH INFINITELY MANY AUTOMORPHISMS

Departamento de Matemáticas
09340, México D.F., México
CINVESTAV IPN
Departamento de Control Automático
07000, México, D.F., México

Abstract. Let be a separable geometric extension such that the pole divisor of is ramified. Let be a function field of genus at least one such that is infinite. If is elliptic we suppose that the characteristic is zero. The main result of the paper is that there are infinitely many non-isomorphic function fields over such that is a Galois extension and .

AMS Subject Classification: 11R58, 11R32, 12F12, 14H52

Key Words and Phrases: inverse Galois problem, geometric extension, infinite automorphism group, moduli field, -improvement