On 4-dimensional translation planes admitting a Suzuki group as group of automorphisms (Q793333)

A translation plane \({\mathcal F}\) is considered as a pair (V,\({\mathcal N})\) consisting of a vector space V and a spread \({\mathcal N}\), that is, a system of half-dimensional subspaces of V covering the space disjointly. Automorphisms of \({\mathcal F}\) are semilinear mappings of V which leave \({\mathcal N}\) invariant. Translation planes can be constructed by taking a group G and checking those G-modules, which are small relative to \(| G|\), for the existence of G-invariant spreads. The explicit description of N is then given by the permutation action of G. In this paper, the author uses as G a subgroup of GL(4,K), isomorphic to \(Sz(2^ r)\), r odd, K a field. The module and the geometric action of G are being completely determined.