2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71569Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be ``large.'' For a fixed $α\in \Q - \Z_{<0}$, Filaseta and Lam have shown that the $n$th degree Generalized Laguerre Polynomial $L_n^{(α)}(x) = \sum_{j=0}^n \binom{n+α}{n-j}(-x)^j/j!$ is irreducible for all large enough $n$. We use our criterion to show that, under these conditions, the Galois group of $\La$ is either the alternating or symmetric group on $n$ letters, generalizing results of Schur for $α=0,1$.6 pagesNumber Theory11R32; 11R09text