WILD RAMIFICATION BOUNDS AND SIMPLE GROUP GALOIS EXTENSIONS RAMIFIED ONLY AT 2

We consider finite Galois extensions of Q(p) and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that; there are no Galois extensions of Q, unramified outside of {2, infinity}, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.