Affiliation:
1. Institut für Analysis und Zahlentheorie, Graz University of Technology, Kopernikusgasse 24/II, 8010 Graz, Austria
Abstract
We show that the Galois group of the polynomial in the title is isomorphic to the full symmetric group on six symbols for all but finitely many [Formula: see text]. This complements earlier work of Filaseta and Moy, who studied Galois groups of [Formula: see text] for more general pairs [Formula: see text], but had to admit a possibly infinite exceptional set specifically for [Formula: see text] of at most logarithmic growth in [Formula: see text]. The proof rests upon invoking Faltings’ theorem on a suitable fibration of Galois resolvents to show that this exceptional set is, in fact, finite.
Funder
Austrian Science Fund
Agence Nationale de la Recherche
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory