  We prove a result about reducibility behaviour of Thue polynomials over the
rationals that was conjectured by M\"uller. 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
M\"uller and Langmann. 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).
