Double transitivity of Galois groups of trinomials
S. D. Cohen, A. Movahhedi, A. Salinier (1997)
Acta Arithmetica
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S. D. Cohen, A. Movahhedi, A. Salinier (1997)
Acta Arithmetica
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Spearman, Blair K., Williams, Kenneth S., Yang, Qiduan (2007)
International Journal of Mathematics and Mathematical Sciences
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Stephen Cohen (1970)
Acta Arithmetica
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Peter Müller (2002)
Annales de l’institut Fourier
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Let be a number field, its ring of integers, and be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations such that is still irreducible. In this paper we study the set of those with reducible. We show that is a finite set under rather weak assumptions. In particular, previous results obtained by diophantine approximation techniques, appear as special cases of some of our results. Our method is different. We use elementary...
Farshid Hajir (2005)
Journal de Théorie des Nombres de Bordeaux
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Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed , Filaseta and Lam have shown that the th degree Generalized Laguerre Polynomial is irreducible for all large enough . We use our criterion to show that, under these conditions, the Galois group of is either the alternating or symmetric group on letters, generalizing results of Schur for .
Charles Parry (1971)
Acta Arithmetica
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Andrzej Schinzel (1966)
Acta Arithmetica
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