  Ideas and techniques from Khare's and Wintenberger's article on the proof of
Serre's conjecture for odd conductors are used to establish that for a fixed
prime l infinitely many of the groups PSL_2(F_{l^r}) (for r running) occur as
Galois groups over the rationals such that the corresponding number fields are
unramified outside a set consisting of l, the infinite place and only one other
prime.
