While disproving a conjecture of Cohen about monodromy groups of polynomials and applying this to give new counter--examples 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 Q of odd square degree n with geometric and arithmetic monodromy group the alternating group A_n and symmetric group S_n, respectively. In this note we give two different proofs that such polynomials do not exist.
Back to Homepage.