Groups of Maximal Arcs

Apart from hyperovals and their duals there are only three classes of maximal arcs known in Desarguesian projective planes. Two classes are due to J. A. Thas and one to R. H. F. Denniston. In this paper collineation stabiliser and isomorphism problems for those maximal arcs in Desarguesian projective planes are examined. The full collineation stabilisers of the known maximal arcs are calculated, and it is shown that all of one class of Thas maximal arcs and those of the second class of Thas maximal arcs in Desarguesian projective planes arising from elliptic quadrics are isomorphic to those of Denniston. The final result is to classify maximal arcs in Desarguesian projective planes whose collineation stabilisers are transitive on the points of the maximal arcs.