Title A family of geometries related to the Suzuki Tower
Author D. Leemans
Reference Comm. Algebra 33 (2005), nr. 7, 2201-2217.
Abstract Michio Suzuki constructed a sequence of five simple groups and graphs which are included in each other. The largest group 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 earlier work, we constructed a rank four geometry G(HJ) on which the Hall-Janko sporadic simple group acts flag-transitively and residually weakly primitively. In this paper, we show that G(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.

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