Proceedings of the Japan Academy, Series A, Mathematical Sciences

On a Galois group arising from an iterated map

Masamitsu Shimakura

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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 $\sigma(x) = x^{3} + ax$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 94, Number 5 (2018), 43-48.

Dates
First available in Project Euclid: 27 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1524794414

Digital Object Identifier
doi:10.3792/pjaa.94.43

Subjects
Primary: 11R32: Galois theory
Secondary: 12F10: Separable extensions, Galois theory 12F20: Transcendental extensions

Keywords
Dynatomic polynomial Galois group

Citation

Shimakura, Masamitsu. On a Galois group arising from an iterated map. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 5, 43--48. doi:10.3792/pjaa.94.43. https://projecteuclid.org/euclid.pja/1524794414


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