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Transactions of the American Mathematical Society

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

 

 

On the inverse problem of Galois theory


Author: J. Kovacic
Journal: Trans. Amer. Math. Soc. 207 (1975), 375-390
MSC: Primary 12F10
DOI: https://doi.org/10.1090/S0002-9947-1975-0379452-1
MathSciNet review: 0379452
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Abstract: Let $ k$ be a field, $ F$ a finite subfield and $ G$ a connected solvable algebraic matric group defined over $ F$. Conditions on $ G$ and $ k$ are given which ensure the existence of a Galois extension of $ k$ with group isomorphic to the $ F$-rational points of $ G$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0379452-1
Keywords: Galois theory, inverse problem in Galois theory, Kummer theory, Frobenius automorphism
Article copyright: © Copyright 1975 American Mathematical Society