On the universal embedding of the near-hexagon for \(U_ 4(3)\)
The author determines the dimension of a vector space \(V\) over \({\mathcal F}_2\) such that there is a (universal) embedding of near-hexagon geometry \(\Gamma\) for \(U_4(3)\) in \(V\). Thus the geometry \(\Gamma\) is defined as a structure with 6-frames as points and 2-frames as lines in a vector space \({\mathcal F}^6_3\) equipped with the form \(q\) defined by \(q(x) = \sum^6_{i = 1} x^2_i\). Author (re-)proves that \(\dim V \leq 21\) using quite elementary techniques of linear algebra and studying in more details suborbits of the geometry \(\Gamma\) and connected components of points in each suborbit.
scientific article; zbMATH DE number 806242