Some results on Tits' geometries of type F<sub>4</sub>


It is known that all finite thick geometries of type C<sub>n</sub> (n≥ 4) with known parameters are buildings (see [10] and [6]).Several facts suggest the conjecture that the same holds in general.Moreover, a finite thick geometry of type F<sub>4</sub> with known parameters is a building unless its parameters are as below (see[6]). It is sensible to conjecture that all finite thick geometries of type F<sub>4</sub> are buildings.I am not able to prove this conjecture.But I collect in this paper some partial results related to this problem.They improve other results given in [9] and [6].

DOI Code: 10.1285/i15900932v5n1p51

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.