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• W3215744144 abstract "Suppose $L/F$ is a finite extension of fields of characteristic 0. We study when $L$ can be defined by an irreducible power compositional polynomial; that is, a polynomial of the form $f(x^k)in F[x]$. If $L$ contains the $k$th roots of unity, then Kummer theory provides an answer. In this case, $f(x^k)$ can be constructed explicitly using automorphisms of $L/F$. If $L$ does not contain the $k$th roots of unity, we use a result of Kang to give a complete answer when $k=3$ and $[L:F]=6$, and we construct a polynomial $x^6+ax^3+b$ defining $L/F$. As an application, we give a simple method for determining the Galois group of an irreducible polynomial $x^6+ax^3+bin F[x]$." @default.
• W3215744144 created "2021-12-06" @default.
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• W3215744144 date "2021-11-01" @default.
• W3215744144 modified "2023-09-27" @default.
• W3215744144 title "Field Extensions Defined by Power Compositional Polynomials" @default.
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• W3215744144 doi "https://doi.org/10.35834/2021/3302163" @default.
• W3215744144 hasPublicationYear "2021" @default.
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