(An,Sn) Realizations by Polynomials—On a Question of Fried

While disproving a conjecture of Cohen about monodromy groups of polynomials and applying this to give new counterexamples to a question of Chowla and Zassenhaus in an earlier paper (1995, M. Fried,Finite Fields Appl.,1, 326–359), Fried asked whether there are polynomials over of odd square degreenwith geometric and arithmetic monodromy group the alternating groupAnand symmetric groupSn, respectively. In this note we give two different proofs that such polynomials do not exist.