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European Journal of Combinatorics
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European Journal of Combinatorics
Article . 1992
License: Elsevier Non-Commercial
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European Journal of Combinatorics
Article . 1992 . Peer-reviewed
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Finite locally generalized quadrangles with affine planes

Authors: Cuypers, F.G.M.T.;

Finite locally generalized quadrangles with affine planes

Abstract

The first author and \textit{A. Pasini} [Eur. J. Comb. 13, No. 1, 39-57 (1992; Zbl 0749.51005)] characterized standard quotients of affine polar spaces of at least rank 4 (an affine polar space is a polar space with a geometric hyperplane removed; a standard quotient of it is a quotient w.r.t. to a group ``fixing the deleted geometric hyperplane'' pointwise). The main result of the paper under review is to extend this result to the rank 3 case (but only in the finite case). Basically, the author shows that every connected finite partial linear space containing affine planes and such that the set of lines and affine planes through any point forms a generalized quadrangle, is a standard quotient of a finite rank 3 affine polar space.

Keywords

Polar geometry, symplectic spaces, orthogonal spaces, standard quotient, Computational Theory and Mathematics, generalized quadrangle, Geometry and Topology, Generalized quadrangles and generalized polygons in finite geometry, affine polar space, Theoretical Computer Science

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Top 10%
Top 10%
hybrid