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A class of exceptional polynomials


Authors: Stephen D. Cohen and Rex W. Matthews
Journal: Trans. Amer. Math. Soc. 345 (1994), 897-909
MSC: Primary 11T06
DOI: https://doi.org/10.1090/S0002-9947-1994-1272675-0
MathSciNet review: 1272675
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Abstract: We present a class of indecomposable polynomials of non prime-power degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field. The associated geometric monodromy groups are the simple groups $ PS{L_2}({2^k})$, where $ k \geq 3$ and odd. (The first member of this class was previously found by P. Müller [17]. This realises one of only two possibilities for such a class which remain following deep work of Fried, Guralnick and Saxl [7]. The other is associated with $ PS{L_2}({3^k})$, $ k \geq 3$ , and odd in fields of characteristic 3.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1272675-0
Keywords: Exceptional polynomials, permutation polynomials, finite fields
Article copyright: © Copyright 1994 American Mathematical Society

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