Hajir, F2024-04-262024-04-262005-01-01https://hdl.handle.net/20.500.14394/34210<p>This is the pre-published version harvested from ArXiv. The published version is located at http://jtnb.cedram.org/item?id=JTNB_2005__17_2_517_0</p> <p>http://archive.numdam.org/ARCHIVE/JTNB/JTNB_2005__17_2/JTNB_2005__17_2_517_0/JTNB_2005__17_2_517_0.pdf</p>Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed α∈ℚ-ℤ <0 , Filaseta and Lam have shown that the nth degree Generalized Laguerre Polynomial L n (α) (x)=∑ j=0 n 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 L n (α) (x) is either the alternating or symmetric group on n letters, generalizing results of Schur for α=0,1,±1 2,-1-n.Galois groupGeneralized Laguerre PolynomialNewton Polygonarticle