Abstract
Let G be a collineation group of a generalized (2n + 1 )-gon Γ and let L be a line such that every symmetry σ of any ordinary (2n + 1 )-gon in Γ containing L with σ(L) = L extends uniquely to a collineation in G. We show that Γ is then a Desarguesian projective plane. We also describe the groups G that arise. As a corollary, we treat the analogous problem without the restriction σ(L) = L.
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A. Kreuzer
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Grundhöfer, T., Van Maldeghem, H. Sharp homogeneity in affine planes, and in some affine generalized polygons. Abh.Math.Semin.Univ.Hambg. 74, 163–174 (2004). https://doi.org/10.1007/BF02941532
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DOI: https://doi.org/10.1007/BF02941532