A combinatorial approach to doubly transitive permutation groups Original Research Article

Let G be a doubly but not triply transitive group on a set X. We give an algorithm to construct the orbits of G acting on image by combining those of its stabilizer H of a point of X If the group H is given first, we compute the orbits of its transitive extension G, if it exists. We apply our algorithm to image and image, image, successfully. We go forward to compute the transitive extension of G itself. In our construction we use a superscheme defined by the orbits of H on image and do not use group elements.