Stable (and good) reduction of three point covers

Abstract If f: Y --> X is a three-point G-Galois cover of the projective line over a p-adic field, then it has good reduction when |G| is prime to p. When p divides |G|, the cover may no longer have good reduction, but there is at least a stable model. We prove some properties of the stable model of f when |G| has a cyclic p-Sylow group. When f is defined over a "small" field, we show that it is impossible for these properties to be satisfied, and thus that f must have good reduction.