On a rank four geometry for the Hall-Janko sporadic group

摘要

Starting from the well-known rank three graph of degree 63 on 100 points associated to the Hall-Janko group J(2), we construct a rank four residually connected and firm geometry Gamma on which J(2) acts flag-transitively and residually weakly primitively (RWPRI). It is the first rank four geometry satisfying RWPRI that is currently known for J(2) and it shows that the RWPRI rank of J(2) is at least four. The diagram of Gamma is the following: [GRAPHICS] (C) 2003 Elsevier Science (USA). All rights reserved. [References: 7]