A CLASS OF EXCEPTIONAL POLYNOMIALS

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 PSL2(2k), where k greater-than-or-equal-to 3 and odd. (The first member of this class was previously found by P. Muller [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 PSL2(3k), k greater-than-or-equal-to 3, and odd in fields of characteristic 3.