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 , where 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 , , 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