Finite Flag-Transitive Geometry of Extended G2-Type

摘要

An explicit construction of a finite flag-transitive geometry of the kind of geometries that are almost buildings (GAB) is given. It is characterized by an extended G2 diagram having the group G2(3) as automorphism group. The geometries of G2-type and the geometry of nonisotropic points in three dimensional unitary space are defined. The octaves and the G2 generalized hexagon and the construction of the extended G2 geometry of order 2 are discussed. It is shown that in the present case the intersection property is satisfied.