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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Automorphism scheme of a finite field extension
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by Pedro J. Sancho de Salas PDF
Trans. Amer. Math. Soc. 352 (2000), 595-608 Request permission

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
  • 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.
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 595-608
  • MSC (1991): Primary 14L27
  • DOI: https://doi.org/10.1090/S0002-9947-99-02361-2
  • MathSciNet review: 1615958