On the subplanes of the Hughes planes of odd square prime order

Abstract

In this paper we give a construction of a family of Baer subplanes of the Hughes plane $\mathbf{\text{H}}$ of odd square prime order $q^2,q\ge 5$, which are not isomorphic to its well-known desarguesian Baer subplane ${\mathbf{\text{H}}}_0[1,5.4]$.