Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles
Copyright policy )Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles
The authors give a very readable description of the history of generalized quadrangles which satisfy the Moufang condition, or some weaker condition, up to 2003. Moreover, they classify all finite thick generalized quadrangles which are quasi-transitive (this is a natural transitivity condition for generalized homologies). As a consequence they obtain the following result (without using the classification of finite simple groups): A finite thick generalized quadrangle is classical or dual classical if and only if it admits a BN-pair and a non-trivial homology.
- Ghent University Belgium
k-Moufang generalized quadrangle, Elation generalized quadrangle, Finite automorphism groups of algebraic, geometric, or combinatorial structures, generalized quadrangle, BN-pair, Group actions on designs, etc., Moufang quadrangle, Linear algebraic groups over arbitrary fields, Theoretical Computer Science, Groups with a \(BN\)-pair; buildings, Quasi-transitive generalized quadrangle, Discrete Mathematics and Combinatorics, Combinatorial aspects of finite geometries, Generalized quadrangles and generalized polygons in finite geometry, Moufang condition, Infinite automorphism groups
k-Moufang generalized quadrangle, Elation generalized quadrangle, Finite automorphism groups of algebraic, geometric, or combinatorial structures, generalized quadrangle, BN-pair, Group actions on designs, etc., Moufang quadrangle, Linear algebraic groups over arbitrary fields, Theoretical Computer Science, Groups with a \(BN\)-pair; buildings, Quasi-transitive generalized quadrangle, Discrete Mathematics and Combinatorics, Combinatorial aspects of finite geometries, Generalized quadrangles and generalized polygons in finite geometry, Moufang condition, Infinite automorphism groups
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