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

Part of: Field extensions Curves

Published online by Cambridge University Press:  14 May 2010

C. ÁLVAREZ-GARCÍA  and
G. VILLA-SALVADOR
C. ÁLVAREZ-GARCÍA
Affiliation:
Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del I.P.N., Av. Instituto Politécnico Nacional No. 2508, Col San Pedro Zacatenco, C.P. 07360, México D. F., México Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, México (email: calvarez@ctrl.cinvestav.mx)
G. VILLA-SALVADOR*
Affiliation:
Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del I.P.N., Av. Instituto Politécnico Nacional No. 2508, Col San Pedro Zacatenco, C.P. 07360, México D. F., México Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, México (email: gvilla@ctrl.cinvestav.mx)
*
✉For correspondence; e-mail: gvilla@ctrl.cinvestav.mx
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Abstract

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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.

Keywords

automorphism groupsfunction fieldsinfinite field of constantsnonseparably generated function fields

MSC classification

Secondary: 12F12: Inverse Galois theory 12F10: Separable extensions, Galois theory 14H05: Algebraic functions; function fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 3 , June 2010 , pp. 301 - 312
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

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