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FINITE GROUPS AS GALOIS GROUPS OF FUNCTION FIELDS WITH INFINITE FIELD OF CONSTANTS
Published online by Cambridge University Press: 14 May 2010
Abstract
Let E/k be a function field over an infinite field of constants. Assume that E/k(x) is a separable extension of degree greater than one such that there exists a place of degree one of k(x) ramified in E. Let K/k be a function field. We prove that there exist infinitely many nonisomorphic separable extensions L/K such that [L:K]=[E:k(x)] and AutkL=AutKL≅Autk(x)E.
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- Copyright © Australian Mathematical Publishing Association Inc. 2010