Large 2-groups of automorphisms of algebraic curves over a field of characteristic 2

Let S be a 2-subgroup of the K-automorphism group Aut(X) of an algebraic curve X of genus g(X) defined over an algebraically closed field K of characteristic 2. It is known that S may be quite large compared to the classical Hurwitz bound 84(g(X)−1). However, if S fixes no point, then the size of S is smaller than or equal to 4(g(X)−1). In this paper, we investigate algebraic curves X with a 2-subgroup S of Aut(X) having the following properties: