Some Equations Over Finite Fields Related to Simple Groups of Suzuki and Ree Types

Abstract

We point out some common features (many valid for admissible infinite fields) of Suzuki and Ree groups (Propositions ??, ?? and Sect. ??.C,E,F), leading to a proof of the uniqueness, up to conjugacy, of ² B ₂(2^{2n + 1}) in B ₂(2^{2n + 1}), ² G ₂(3^{2n + 1}) in G ₂(3^{2n + 1}) and the possibilities for the structure of the normalizer in F ₄(2^{2n + 1}) of the centre of a Sylow 2-subgroup of ² F ₄(2^{2m + 1}).

Subject Classifications: 20E, 20G