On the inverse problem of Galois theory

Kovacic, J.

doi:10.1090/S0002-9947-1975-0379452-1

On the inverse problem of Galois theory
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Trans. Amer. Math. Soc. 207 (1975), 375-390 Request permission

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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Lectures on algebraic groups

Zyklische Körper und Algebren der Charackteristik $p$ vom Grad

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