A class of exceptional polynomials

Cohen, Stephen D.; Matthews, Rex W.

doi:10.1090/S0002-9947-1994-1272675-0

A class of exceptional polynomials
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by Stephen D. Cohen and Rex W. Matthews

Trans. Amer. Math. Soc. 345 (1994), 897-909

DOI: https://doi.org/10.1090/S0002-9947-1994-1272675-0

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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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