Symplectic geometries, transvection groups, and modules
type: Item
instance of: scholarly article
title: Symplectic geometries, transvection groups, and modules
zbMATH Open document ID: 0824.51003
DOI: 10.1016/0097-3165(94)90036-1
author: Hans Cuypers
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-03-24T00:00:00Z
review text: Let \((P,L)\) be a connected partial linear space in which any pair of intersecting lines is contained in a subspace isomorphic to a symplectic plane. Assume that \((P,L)\) contains at least two such subspaces and a line with more than three points. The author extends to infinite spaces a result of J. I. Hall. He proves that \((P,L)\) is isomorphic to the geometry of hyperbolic lines of a symplectic geometry. Then he uses this to characterize the subgroups of the symplectic group that are generated by transvection subgroups. He also gives a characterization of the natural modules for this groups.
Mathematics Subject Classification ID: 51A50
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 529906
zbMATH Keywords: transvection groups
zbMATH Keywords: geometry of hyperbolic lines
zbMATH Keywords: symplectic geometry
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90036-1
OpenAlex ID: W2142476563
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description: scientific article; zbMATH DE number 529906