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Preprints, Working Papers, ... Year : 2024

ON THE HEIGHT OF SOME GENERATORS OF GALOIS EXTENSIONS WITH BIG GALOIS GROUP

Jonathan Jenvrin

Abstract

We study the height of generators of Galois extensions of the rationals having the alternating group An as Galois group. We prove that if such generators are obtained from certain, albeit classical, constructions, their height tends to infinity as n increases. This provides an analogue of a result by Amoroso, originally established for the symmetric group.
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hal-04485372 , version 1 (01-03-2024)

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Public Domain

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Jonathan Jenvrin. ON THE HEIGHT OF SOME GENERATORS OF GALOIS EXTENSIONS WITH BIG GALOIS GROUP. 2024. ⟨hal-04485372⟩

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