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Constructions of rank five geometries for the Mathieu group M 22
Authors:Dimitri Leemans
Affiliation:(1) Université Libre de Bruxelles, C.P.216-Géométrie, Boulevard du Triomphe, 1050 Bruxelles, Belgium
Abstract:We construct nine rank five incidence geometries that are firm and residually connectedand on which the Mathieu group M22 acts flag-transitively. The constructions usemainly objects arising from the Steiner systemS(3, 6, 22).One of these geometries was constructed by Meixner and Pasini in [10]. Three of themare obtained from the geometry of Meixner and Pasini using doubling (see [8] or [12]) or similar constructions. The remaining five are new and four of them have a star diagram. Theselatter four geometries are constructed using special partitions of the 22 points of the Steiner system S(3, 6, 22).
Keywords:51E24  20D08
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