A Classification of the Veldkamp Lines of the Near Hexagon L3 × GQ(2, 2)

Richard M. Green, Metod Saniga

Abstract


Using a standard technique sometimes (inaccurately) known as Burnside’s Lemma, it is shown that the Veldkamp space of the near hexagon L3 × GQ(2,2) features 156 different types of lines. We also give an explicit description of each type of a line by listing the types of the three geometric hyperplanes it consists of and describing the properties of its core set, that is the subset of points of L3 × GQ(2,2) shared by the three geometric hyperplanes in question.


Keywords


Near hexagons, Geometric hyperplanes, Veldkamp spaces

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications