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Constructions of rank five geometries for the Mathieu group M22

par Leemans, Dimitri
Référence Journal of geometry, 79, 1-2, page (146-155)
Publication Publié, 2004

Article révisé par les pairs

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Résumé :

We construct nine rank five incidence geometries that are firm and residually connected and on which the Mathieu group M22 acts flag-transitively. The constructions use mainly objects arising from the Steiner system 5(3, 6, 22). One of these geometries was constructed by Meixner and Pasini in [10]. Three of them are 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. These latter four geometries are constructed using special partitions of the 22 points of the Steiner system S(3, 6, 22). © Birkhäuser Verlag, Basel, 2004.