Geodesic
WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS
Glasgow mathematical journal, Tome 63 (2021) no. 1, pp. 106-120

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DOI

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. 
BENSEBAA, BOUALEM; MOVAHHEDI, ABBAS; SALINIER, ALAIN. WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS. Glasgow mathematical journal, Tome 63 (2021) no. 1, pp. 106-120. doi: 10.1017/S001708952000004X
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     author = {BENSEBAA, BOUALEM and MOVAHHEDI, ABBAS and SALINIER, ALAIN},
     title = {WILD {RAMIFICATION} {IN} {TRINOMIAL} {EXTENSIONS} {AND} {GALOIS} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {106--120},
     year = {2021},
     volume = {63},
     number = {1},
     doi = {10.1017/S001708952000004X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708952000004X/}
}
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