The Classification of Finite Generalized Quadrangles Admitting a Group Acting Transitively on Ordered Pentagons
Copyright policy )The Classification of Finite Generalized Quadrangles Admitting a Group Acting Transitively on Ordered Pentagons
Let \(\mathcal S\) be a thick generalized quadrangle and let \(G\) be a group of automorphisms of \(\mathcal S\). If \(G\) acts transitively on the set of non- degenerate ordered pentagons, then \(\mathcal S\) is one of the classical generalized quadrangles \(W(q)\), \(Q(4,q)\), \(Q(5,q)\) or \(H(3,q^ 2)\). The possibilities for \(G\) in each case are determined. We do not use the classification of the finite simple groups (from which this result also follows).
- Ghent University Belgium
generalized polygons, Finite automorphism groups of algebraic, geometric, or combinatorial structures, generalized quadrangle, Generalized quadrangles and generalized polygons in finite geometry
generalized polygons, Finite automorphism groups of algebraic, geometric, or combinatorial structures, generalized quadrangle, Generalized quadrangles and generalized polygons in finite geometry
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