  We prove the existence of certain rationally rigid triples in F_4(p) for good
primes p (i.e., p>3), thereby showing that these groups occur as regular Galois
groups over Q(t) and so also over Q. We show that these triples give rise to
rigid triples in the algebraic group and prove that they generate an
interesting subgroup in characteristic 0.

Number Theory;Group Theory;Representation Theory