1,721,663 research outputs found
Parallelisms and cubes in C2.c-geometries
No full textWe characterize C-2.c-geometries that are truncations of almost-thin C-n-geometries and C-2.c-geometries covered by truncated almost-thin buildings of type C-n. Then we show how to profit from those characterizations in the investigation of a number of special cases. The proof of our main theorem is a rearrangement of the proof of a theorem by Brouwer on rectagraphs. A generalization of Brouwer's theorem is also given. (C) 1998 Academic Press Limited
Diagram geometries for sharply n-transitive sets of permutations or of mappings
No full textA characterization of sharply n-transitive sets of permutations or of mappings is given by means of Buekenhout diagrams. As a by-product, a characterization is obtained in the same style for finite Minkowski and Laguerre planes. Two preliminary results are used to obtain these diagram-theoretic descriptions. One of them gives us a characterization of the complement of a square lattice graph by means of the nonexistence of certain configurations. The other one states that every net of degree s + 1 with s + 2 points on each line is embeddable in a projective plane of order s + 2. This latter result is exploited to get control over the geometries appearing as rank 2 residues on top in the diagrams we consider. Next, we can use the earlier result to obtain the information we need on the point-graphs of the geometries we want to describe. © 1992 Kluwer Academic Publishers
On a problem on chamber systems
No full textIt is well known that a geometry belonging to a disconnected diagram is the direct sum of geometries corresponding to the connected components of the diagram. On the other hand, chamber systems with a disconnected diagram exist which do not split as direct products of components of smaller rank. Many finite examples of this kind are discussed in Groups of Lie Type and their Geometries (CUP, 1995, pp. 185-214), but none of them is simply connected. In this article, we construct a simply connected finite example
A characterization of truncated projective gometries as flag-transitive PG*.PG-geometries
No full textWe prove that every flag-transitive locally finite (PG*.PG)-geometry is a truncated projective geometry. © 2007 Springer Science+Business Media, LLC
On locally polar spaces whose planes are affine
No full textWe give some contributions to the classification of geometries belonging to the following diagram: (Af. Cn) © 1990 Kluwer Academic Publishers
Geometries of type Cn and F4 with lag-transitive automrphism groups
No full textLet G{cyrillic} be a finite thick geometry of type Cn (n ≥ 4) or F4. We prove that G{cyrillic} is a building iff Aut(G{cyrillic}) is flag-transitive. © 1988 D. Reidel Publishing Company
Embeddings and expansions
No full textIn this paper we sketch a general theory of embeddings for geometries with string diagrams, focusing on their hulls. An affine-like geometry, which we call expansion, is associated to every embedding. As we shall prove, the universal cover of the expansion of an embedding is the expansion of the hull of that embedding. Some applications of this theorem are given
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