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De Bruyn, Bart; Shpectorov, Sergey

The hyperplanes of the \(U_{4}(3)\) near hexagon. (English) Zbl 1230.05294

Graphs Comb. 26, No. 5, 647-671 (2010).
Summary: Combining theoretical arguments with calculations in the computer algebra package GAP, we are able to show that there are 27 isomorphism classes of hyperplanes in the near hexagon for the group \(U_{4}(3)\). We give an explicit construction of a representative of each class and we list several combinatorial properties of such a representative.

Cited in 4 Documents

MSC:

05E18 Group actions on combinatorial structures
51A45 Incidence structures embeddable into projective geometries
51A50 Polar geometry, symplectic spaces, orthogonal spaces
51E12 Generalized quadrangles and generalized polygons in finite geometry
68W30 Symbolic computation and algebraic computation

Keywords:

near hexagon; hyperplane; dual polar space; universal embedding; minimal full polarized embedding

Software:

GAP
Cite Review PDF
Full Text: DOI

References:

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