On a Geometry of Ivanov and Shpectorov for the O'Nan Sporadic Simple Group

We show that, for the O'Nan sporadic simple group, there is no Rwpri and (IP)2 geometry of rank 6 with a maximal parabolic subgroup isomorphic to M11 and that there is no Rwpri and (IP)2 geometry of rank 5 with a maximal parabolic subgroup isomorphic to J1 . This last result permits us to show that the Ivanov Shpectorov geometry is not Rwpri. The results obtained in this paper rely partially on computer algebra. 1999 Academic Press