Symplectic geometries, transvection groups, and modules

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We show that any connected partial linear space in which there is a line with at least four points and that has the property that any pair of intersecting lines is contained in a subspace isomorphic to a symplectic plane is isomorphic to the geometry of hyperbolic lines in some symplectic geometry. As a corollary to this result we obtain a characterization of the subgroups of the symplectic groups that are generated by transvection subgroups. Also a characterization of the natural modules for these groups is obtained.
Original languageEnglish
Pages (from-to)39-59
Number of pages21
JournalJournal of Combinatorial Theory, Series A
Issue number1
Publication statusPublished - 1994


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