  For each odd prime power q, we construct an infinite sequence of rational
functions f(X) in F_q(X), each of which is exceptional, which means that for
infinitely many n the map c-->f(c) induces a bijection of P^1(F_{q^n}).
Moreover, each of our functions f(X) is indecomposable, which means that it
cannot be written as the composition of lower-degree rational functions in
F_q(X). In case q is not a power of 3, these are the first known examples of
indecomposable exceptional rational functions f(X) over F_q which have
non-solvable monodromy groups and have arbitrarily large degree. These are also
the first known examples of wildly ramified indecomposable exceptional rational
functions f(X), other than linear changes of polynomials.

Number Theory