On a Galois group arising from an iterated map

On a Galois group arising from an iterated map

We study the irreducibility and the Galois group of the polynomial f(a,x) = [x.sup.8] + 3a[x.sup.6] + 3[a.sup.2][x.sup.4] + ([a.sup.2] + 1)a[x.sup.2] + [a.sup.2] + 1 over Q(a) and Q. This polynomial is a factor of the 4-th dynatomic polynomial for the map [sigma](x) = [x.sup.3] + ax. Key words: Dyna...

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Veröffentlicht in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2018-05, Vol.94 (5), p.43-48
1. Verfasser: Shimakura, Masamitsu
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Groups (Mathematics)
Maps (Mathematics)
Polynomials
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Beschreibung
Zusammenfassung:We study the irreducibility and the Galois group of the polynomial f(a,x) = [x.sup.8] + 3a[x.sup.6] + 3[a.sup.2][x.sup.4] + ([a.sup.2] + 1)a[x.sup.2] + [a.sup.2] + 1 over Q(a) and Q. This polynomial is a factor of the 4-th dynatomic polynomial for the map [sigma](x) = [x.sup.3] + ax. Key words: Dynatomic polynomial; Galois group.
ISSN:0386-2194
DOI:10.3792/pjaa.94.43