Of finite geometries of type
with thick lines
Abstract
Several facts suggest the conjecture that every finite geometry of type
with thick lines is either a bulding or flat ( see [4] , [5] , [8] and [9]). That conjecture plays a central role in the problem of classifying finite thick geometries of type
and
( see [4] , [7] and [8] ).In this paper we find very simple conditions that hold in a finite geometry of type
with thick lines if and only if the geometry is either a building or flat. Then the previous conjecture can be restated so: prove that the conditions discussed in this paper are theorems in the case of finite geometries with thick lines.
![C<sub>3</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8374cf3267f97782ea695a567a926c2f.png)
![C<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/50f922c394e1c7e709c9d60940a1b478.png)
![F<sub>4</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/539a7b58f8ba609b7b8d36a54415874e.png)
![C<sub>3</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8374cf3267f97782ea695a567a926c2f.png)
DOI Code:
10.1285/i15900932v6n2p205
Full Text: PDF