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Automorphism scheme of a finite field extension


Author: Pedro J. Sancho de Salas
Journal: Trans. Amer. Math. Soc. 352 (2000), 595-608
MSC (1991): Primary 14L27
DOI: https://doi.org/10.1090/S0002-9947-99-02361-2
Published electronically: May 3, 1999
MathSciNet review: 1615958
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Abstract: Let $k\to K$ be a finite field extension and let us consider the automorphism scheme $Aut_kK$. We prove that $Aut_kK$ is a complete $k$-group, i.e., it has trivial centre and any automorphism is inner, except for separable extensions of degree 2 or 6. As a consequence, we obtain for finite field extensions $K_1, K_2$ of $k$, not being separable of degree 2 or 6, the following equivalence:

\begin{equation*}K_1\simeq K_2 \Leftrightarrow Aut_kK_1\simeq Aut_kK_2.\end{equation*}


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Additional Information

Pedro J. Sancho de Salas
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Badajoz 06071, Spain
Email: sancho@unex.es

DOI: https://doi.org/10.1090/S0002-9947-99-02361-2
Keywords: Finite field extension, automorphism, complete
Received by editor(s): October 31, 1997
Published electronically: May 3, 1999
Additional Notes: This paper is part of the author’s dissertation at the Universidad de Salamanca under the supervision of J. B. Sancho de Salas.
Article copyright: © Copyright 1999 American Mathematical Society

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