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FINITE GROUPS AS GALOIS GROUPS OF FUNCTION FIELDS WITH INFINITE FIELD OF CONSTANTS

  • C. ÁLVAREZ-GARCÍA (a1) (a2) and G. VILLA-SALVADOR (a1) (a3)

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=AutKLAutk(x)E.

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Copyright

Corresponding author

For correspondence; e-mail: gvilla@ctrl.cinvestav.mx

References

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[1]Álvarez-García, C. and Villa-Salvador, G., ‘Groups of automorphisms of global function fields’, Int. J. Algebra 2 (2008), 6578.
[2]Deuring, M., Lectures on the Theory of Algebraic Functions of One Variable, Lecture Notes in Mathematics, 314 (Springer, Berlin, 1973).
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[5]Madan, M. and Rosen, M., ‘The automorphism group of a function field’, Proc. Amer. Math. Soc. 115 (1992), 923929.
[6]Madden, D. J. and Valentini, R. C., ‘The group of automorphisms of algebraic function fields’, J. Reine Angew. Math. 343 (1983), 162168.
[7]Rzedowski-Calderón, M. and Villa-Salvador, G., ‘Automorphisms of congruence function fields’, Pacific J. Math. 150 (1991), 167178.
[8]Stichtenoth, H., ‘Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper’, Math. Z. 187 (1984), 221225.
[9]Stichtenoth, H., Algebraic Function Fields and Codes, Universitext (Springer, Berlin, 1993).
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