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May 2018 On a Galois group arising from an iterated map
Masamitsu Shimakura
Proc. Japan Acad. Ser. A Math. Sci. 94(5): 43-48 (May 2018). DOI: 10.3792/pjaa.94.43

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

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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

Information

Published: May 2018
First available in Project Euclid: 27 April 2018

zbMATH: 06941820
MathSciNet: MR3795746
Digital Object Identifier: 10.3792/pjaa.94.43

Subjects:
Primary: 11R32
Secondary: 12F10 , 12F20

Keywords: Dynatomic polynomial , Galois group

Rights: Copyright © 2018 The Japan Academy

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Vol.94 • No. 5 • May 2018
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