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WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS

Published online by Cambridge University Press:  12 March 2020

BOUALEM BENSEBAA
Affiliation:
Laboratoire LA3C, Faculté de Mathématiques, USTHB, Bab Ezzouar 16111, Algeria, e-mail: b.benseba@usthb.dz
ABBAS MOVAHHEDI
Affiliation:
XLIM (UMR 7252 CNRS, Université de Limoges), 87060 Limoges Cedex, France, e-mails: abbas.movahhedi@unilim.fr, alain.salinier@unilim.fr
ALAIN SALINIER
Affiliation:
XLIM (UMR 7252 CNRS, Université de Limoges), 87060 Limoges Cedex, France, e-mails: abbas.movahhedi@unilim.fr, alain.salinier@unilim.fr

Abstract

It is proven that, for a wide range of integers s (2 < s < p − 2), the existence of a single wildly ramified odd prime lp leads to either the alternating group or the full symmetric group as Galois group of any irreducible trinomial Xp + aXs + b of prime degree p.

Type
Research Article
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS
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