On a Geometry of Ivanov and Shpectorov for the OʹNan Sporadic Simple Group

We show that, for the OʹNan sporadic simple group, there is noRwpriand (IP)2geometry of rank 6 with a maximal parabolic subgroup isomorphic toM11and that there is noRwpriand (IP)2geometry of rank 5 with a maximal parabolic subgroup isomorphic toJ1. This last result permits us to show that the Ivanov– Shpectorov geometry is notRwpri. The results obtained in this paper rely partially on computer algebra.