On the reducibility behavior of Thue polynomials.

We prove a result about reducibility behavior of Thue polynomials over the rationals that was conjectured in [7] . More precisely, we show that, apart from few explicitly given exceptions, these polynomials have only finitely many reducible integer specializations. Special cases have been proved e.g. by Müller in [7] , Theorem 4.9, and Langmann [6, Satz 3.5] . The proof uses ramification theory to reduce the assertion to a statement about permutation groups containing an n -cycle. This statement is finally proven with the help of the classification of primitive permutation groups containing an n -cycle (a result which rests on the classification of finite simple groups). [ABSTRACT FROM AUTHOR]