2023
DOI: 10.1142/s1793042123501208
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Galois groups of n 0 + n 1 X + ⋯ + n 6 X6

Benjamin Klahn,
Marc Technau

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 … Show more

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