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WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS

Part of: Field extensions General field theory Algebraic number theory: global fields Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  12 March 2020

BOUALEM BENSEBAA ,
ABBAS MOVAHHEDI  and
ALAIN SALINIER
BOUALEM BENSEBAA
Affiliation:
Laboratoire LA3C, Faculté de Mathématiques, USTHB, Bab Ezzouar16111, Algeria, e-mail: b.benseba@usthb.dz
ABBAS MOVAHHEDI
Affiliation:
XLIM (UMR 7252 CNRS, Université de Limoges), 87060LimogesCedex, France, e-mails: abbas.movahhedi@unilim.fr, alain.salinier@unilim.fr
ALAIN SALINIER
Affiliation:
XLIM (UMR 7252 CNRS, Université de Limoges), 87060LimogesCedex, France, e-mails: abbas.movahhedi@unilim.fr, alain.salinier@unilim.fr
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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 l ≠ p 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.

MSC classification

Primary: 11R32: Galois theory 12F10: Separable extensions, Galois theory
Secondary: 11S15: Ramification and extension theory 12E10: Special polynomials
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 1 , January 2021 , pp. 106 - 120
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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