Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 46, No. 2, pp. 561-574 (2005)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 561-574 (2005) |
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A generalization of a construction due to Van NypelseerDimitri LeemansUniversité Libre de Bruxelles, Département de Mathématique - C.P.216, Boulevard du Triomphe, B-1050 Bruxelles; e-mail: dleemans@ulb.ac.beAbstract: We give a construction leading to new geometries from Steiner systems or arbitrary rank two geometries. Starting with an arbitrary rank two residually connected geometry $\Gamma$, we obtain firm, residually connected, $(IP)_2$ and flag-transitive geometries only if $\Gamma$ is a thick linear space, the dual of a thick linear space or a $(4,3,4)$-gon. This construction is also used to produce a new firm and residually connected rank six geometry on which the Mathieu group ${\sf M}_{24}$ acts flag-transitively. Full text of the article:
Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.
© 2005 Heldermann Verlag
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