  Let k be a perfect field of characteristic p > 0, and let G be a finite
group. We consider the pointed G-curves over k associated by Harbater, Katz,
and Gabber to faithful actions of G on k[[t]] over k. We use such "HKG
G-curves" to classify the automorphisms of k[[t]] of p-power order that can be
expressed by particularly explicit formulas, namely those mapping t to a power
series lying in a Z/pZ Artin-Schreier extension of k(t). In addition, we give
necessary and sufficient criteria to decide when an HKG G-curve with an action
of a larger finite group J is also an HKG J-curve.
