Smooth Hughes planes are classical

We prove that the only compact projective Hughes planes which are smooth projective planes are the classical planes over the complex numbers \Bbb C \Bbb C , the quaternions \Bbb H \Bbb H , and the Caley numbers \Bbb O \Bbb O . As a by-product this shows that an 8-dimensional smooth projective plane which admits a collineation group of dimension d 3 17d \geq 17 is isomorphic to the quaternion projective plane P ₂\Bbb H {\cal P _2\Bbb H }. For topological compact projective planes this is true if d 3 19d \geq 19, and this bound is sharp.