On nilpotent automorphism groups of function fields

We study the automorphisms of a function field of genus g >= 2 over an algebraically closed field of characteristic p > 0. More precisely, we show that the order of a nilpotent subgroup G of its automorphism group is bounded by 16 (g - 1) when G is not a p-group. We show that if |G| = 16(g - 1), then g - 1 is a power of 2. Furthermore, we provide an infinite family of function fields attaining the bound.