On a Galois group arising from an iterated map. (English) Zbl 1418.11146

Summary: We study the irreducibility and the Galois group of the polynomial \(f(a,x)=x^{8}+3ax^{6}+3a^{2}x^{4}+(a^{2}+1)ax^{2}+a^{2}+1\) over \(\mathbb{Q}(a)\) and \(\mathbb{Q}\). This polynomial is a factor of the 4-th dynatomic polynomial for the map \(\sigma(x)=x^{3}+ax\).


11R32 Galois theory
12F10 Separable extensions, Galois theory
12F20 Transcendental field extensions


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