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 M(11) and that there is no RWPRI and (IP)(2) geometry of rank 5 with a maximal parabolic subgroup isomorphic to J(t). 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. (C) 1999 Academic Press.