Beitr\ EMIS ELibM Electronic Journals 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 Nypelseer

Dimitri Leemans

Université Libre de Bruxelles, Département de Mathématique - C.P.216, Boulevard du Triomphe, B-1050 Bruxelles; e-mail:

Abstract: 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.

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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.

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