Constructions of rank five geometries for the Mathieu group M
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Authors: | Dimitri Leemans |
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Institution: | (1) Université Libre de Bruxelles, C.P.216-Géométrie, Boulevard du Triomphe, 1050 Bruxelles, Belgium |
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Abstract: | 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 systemS(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). |
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Keywords: | 51E24 20D08 |
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