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The Hurwitz bound on the size of the ‐automorphism group Aut(χ) of an algebraic curve χ of genus  g  ⩾ 2 defined over a field  of zero characteristic is |Aut(χ)| ⩽ 84( g  − 1). For a positive characteristic, algebraic curves can have many more automorphisms than expected from the Hurwitz bound. There even exist algebraic curves of arbitrary high genus  g  with more than 16 g  4  automorphisms. It has been observed on many occasions that the most anomalous examples of algebraic curves with very large automorphism groups invariably have zero  p ‐rank. In this paper, the ‐automorphism group Aut(χ) of a zero 2‐rank algebraic curve χ defined over an algebraically closed field  of characteristic 2 is investigated. The main result is that, if the curve has genus  g  ⩾ 2 and |Aut(χ)| > 24 g ( g  − 1), then Aut(χ) has a fixed point on χ, apart from a few exceptions. In the exceptional cases, the possibilities for Aut(χ) and  g  are determined.

Automorphism groups of algebraic curves with p ‐rank zero