@article{Ao2022, 
author = {Lingfeng Ao and Shuanglin Fei and Shaofang Hong},
title = {On the Galois group of three classes of trinomials},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {212-224},
keywords = {p-adic Newton polygon, irreducibility criterion, Galois group},
url = {https://www.sciopen.com/article/10.3934/math.2022013},
doi = {10.3934/math.2022013},
abstract = {Let    n  ≥  8 be an integer and let    p be a prime number satisfying        n    2    <  p  <  n  −  2. In this paper, we prove that the Galois groups of the trinomials         T          n      ,      p      ,      k        (  x  )  :=      x    n    +      n    k        p          (      n      −      1      −      p      )      k            x    p    +      n    k        p          n      k        ,         S          n      ,      p        (  x  )  :=      x    n    +      p          n      (      n      −      1      −      p      )            n    p        x    p    +      n    p        p                  n        2            and         E          n      ,      p        (  x  )  :=      x    n    +  p  n      x          n      −      p        +  p      n    2  are the full symmetric group        S    n   under several conditions. This extends the Cohen-Movahhedi-Salinier theorem on the irreducible trinomials    f  (  x  )  =      x    n    +  a      x    s    +  b with integral coefficients.}
}