Geodesic
Determination of generalized quadrangles with distinct elation points
Journal of Algebraic Combinatorics, Tome 24 (2006) no. 1, pp. 5-22.

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Summary: In this paper, we classify the finite generalized quadrangles of order $( s, t), s, t > 1$, which have a line $L$ of elation points, with the additional property that there is a line $M$ not meeting $L$ for which ${ L, M}$ is regular. This is a first fundamental step towards the classification of those generalized quadrangles having a line of elation points.
Classification : 51E12,, 51E20,, 20B25,, 20E42
Keywords: keywords generalized quadrangle, elation generalized quadrangle, translation generalized quadrangle, Moufang condition, symmetry, regularity, classification 
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     title = {Determination of generalized quadrangles with distinct elation points},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2006__24_1_a6/}
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Thas, Koen. Determination of generalized quadrangles with distinct elation points. Journal of Algebraic Combinatorics, Tome 24 (2006) no. 1, pp. 5-22. http://geodesic.mathdoc.fr/item/JAC_2006__24_1_a6/