The Galois groups of the polynomials \(x^ n+ax^ s+b\). II
[For part I, see J. Number Theory 25, 230-238 (1987; Zbl 0608.12010).] This paper gives conditions under which the Galois group of a polynomial \(x^ n+ax^ s+b\) over the rational number field \({\mathbb{Q}}\) is isomorphic to the symmetric group \(S_ n\). Further, this paper gives a criterion for the Galois group of a polynomial over \({\mathbb{Q}}\) to be isomorphic to \(S_ n\) or to \(A_ n\). The author also constructs infinitely many polynomials with the Galois groups \(A_ 4\), \(A_ 5\) and \(A_ 7\).
scientific article; zbMATH DE number 3995826