Michel Raynaud gave a criterion for a three-point G-cover f : Y \rightarrow X
= P^1, defined over a p-adic field K, to have good reduction. In particular, if
the order of a p-Sylow subgroup of G is p, and the number of conjugacy classes
of elements of order p is greater than the absolute ramification index e of K,
then f has potentially good reduction. We give a different proof of this
criterion, which extends to the case where G has an arbitrarily large cyclic
p-Sylow subgroup, answering a question of Raynaud. We then use the criterion to
give a family of examples of three-point covers with good reduction to
characteristic p and arbitrarily large p-Sylow subgroups.Comment: Minor revisions, to appear in Algebraic Geometry. 16 page