# zbMATH — the first resource for mathematics

Flag-transitive Buekenhout geometries. (English) Zbl 0774.51003
Combinatorics ’90, Proc. Conf., Gaeta/Italy 1990, Ann. Discrete Math. 52, 403-447 (1992).
[For the entire collection see Zbl 0748.00018.]
The authors survey some of the classification theorems for some classes of finite geometries belonging to Buekenhout diagrams obtained from Coxeter diagrams replacing some of strokes for projective planes with strokes for circular spaces or for dual circular spaces. They consider the following main themes:
The diagram $$c^ k\cdot A_ m$$.
The diagram $$c\cdot C_{n-1}$$. The plane case.
The diagram $$c \cdot D_{n-1}$$. The plane case.
The diagram $$c^ k \cdot C_ m$$ and $$c^ k \cdots D_ m$$ with $$m \geq 3$$.
The diagram $$c^{n-2} \cdot C_ 2$$. Examples.
The diagram $$c^{n-1} \cdot C_ 2$$. Theorems.
The diagram $$c \cdot A_{n-2} \cdot c^*$$.
Two problems.

##### MSC:
 51E24 Buildings and the geometry of diagrams 20D08 Simple groups: sporadic groups
##### Keywords:
sporadic simple group; finite geometry; Coxeter diagrams