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On a Rank Five Geometry of Meixner for the Mathieu Group M12

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Abstract

We construct a rank five residually connected and firm geometry Γ on which the Mathieu group M 12 acts flag-transitively and residually weakly primitively (RWPRI). The group M 12 is the group of automorphisms of Γ and Aut(M 12) is the correlation group of Γ, in particular Γ is self-dual. The diagram of Γ is the following. Moreover Γ satisfies the conditions (IP)2 and (2T)1. As a corollary, we obtain that the (RWPRI+(IP)2)-rank of M 12 is 5.

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  1. Département de Mathématique, Université Libre de Bruxelles, CP216, Boulevard du Triomphe, B-1050, Brussels, Belgium

    Dimitri Leemans

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  1. Dimitri Leemans
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Leemans, D. On a Rank Five Geometry of Meixner for the Mathieu Group M12. Geometriae Dedicata 85, 273–281 (2001). https://doi.org/10.1023/A:1010320510753

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  • DOI: https://doi.org/10.1023/A:1010320510753

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