Groups of maximal arcs

Apart from hyperovals and their duals there are only three classes of maxim al 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 stabilise r and isomorphism problems for those maximal arcs in Desarguesian projectiv e planes are examined. The Full collineation stabilisers of the known maxim al arcs are calculated. and it is shown that all of one class of Thas maxim al 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 pr ojective planes whose collineation stabilisers are transitive on the points of the maximal arcs. (C) 2001 Academic Press.