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AN INFINITE FAMILY OF NINTH DEGREE DIHEDRAL POLYNOMIALS
Published online by Cambridge University Press: 14 August 2017
Abstract
For any integer $m\neq 0$, we prove that $f(x)=x^{9}+9mx^{6}+192m^{3}$ is irreducible over $\mathbb{Q}$ and that the Galois group of $f(x)$ over $\mathbb{Q}$ is the dihedral group of order 18. Moreover, we show that for infinitely many values of $m$, the splitting fields for $f(x)$ are distinct.
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- Research Article
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- © 2017 Australian Mathematical Publishing Association Inc.
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