Some results on Tits' geometries of type ![F<sub>4</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/539a7b58f8ba609b7b8d36a54415874e.png)
Abstract
It is known that all finite thick geometries of type
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
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
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].
![C<sub>n</sub> (n≥ 4)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/d557fe139e23795dd302abc84790a86e.png)
![F<sub>4</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/539a7b58f8ba609b7b8d36a54415874e.png)
![F<sub>4</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/539a7b58f8ba609b7b8d36a54415874e.png)
DOI Code:
10.1285/i15900932v5n1p51
Full Text: PDF