The stabilizer of the Adelaide oval Original Research Article

Cherowitzo, O’Keefe and Penttila discovered a new family of q-clans, q even, and they gave the name Adelaide to all the new associated geometries, i.e., the generalized quadrangles, the flocks of the quadratic cone, the ovals, etc. Their computations provide a cyclic group of order 2e stabilizing the new Adelaide oval in image, with image. It is the purpose of this paper to show that this stabilizer induced by the collineations of the corresponding generalized quadrangle is in fact the complete stabilizer of the Adelaide oval.