par Leemans, Dimitri
Référence Communications in algebra, 33, 7, page (2201-2217)
Publication Publié, 2005
Article révisé par les pairs
Résumé : Michio Suzuki constructed a sequence of five simple groups Gi, with i = 0,...,4, and five graphs Δi, with i = 0,...,4, such that Δi appears as a subgraph of Δi+1 for i = 0,...,3 and Gi is an automorphism group of Δi for i = 0,...,4. The largest group G4 was a new sporadic group of order 448 345 497 600. It is now called the Suzuki group Suz. These groups and graphs form what Jacques Tits calls the Suzuki tower. In a previous work, we constructed a rank four geometry Γ(HJ) on which the Hall-Janko sporadic simple group acts flag-transitively and residually weakly primitively. In this article, we show that Γ(HJ) belongs to a family of five geometries in bijection with the Suzuki tower. The largest of them is a geometry of rank six, on which the Suzuki sporadic group acts flag-transitively and residually weakly primitively. Copyright © Taylor & Francis, Inc.