Abstract
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 $\mathbf{Q}(a)$ and $\mathbf{Q}$. This polynomial is a factor of the 4-th dynatomic polynomial for the map $\sigma(x) = x^{3} + ax$.
Citation
Masamitsu Shimakura. "On a Galois group arising from an iterated map." Proc. Japan Acad. Ser. A Math. Sci. 94 (5) 43 - 48, May 2018. https://doi.org/10.3792/pjaa.94.43