Two rank six geometries for the Higman-Sims sporadic group

摘要

We construct two rank six geometries that are firm and residually connected and on which the Higman-Sims sporadic group HS acts flag-transitively. Both of these geometries have five rank five residues isomorphic to geometries of the Mathieu group Mj2- They continue chains of geometries obtained for A_5, A_6, L_3(4) and M_(22). Moreover, they are the first rank six geometries constructed for HS.