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Linearly small elation quadrangles

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Abstract

We show that each elation generalized quadrangle with parameters (p, p), where p is a prime, is isomorphic to the symplectic quadrangle W(p) or its dual Q(4, p). Our results cover the more general case of linearly small elation generalized quadrangles. In particular, we obtain a characterization of the symplectic quadrangle over the field of complex numbers among compact connected quadrangles. We prove that every root elation quadrangle (Q, c, H F ) is a skew translation quadrangle.

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  1. Institut für Geometrie und Topologie, Universität Stuttgart, 70550, Stuttgart, Germany

    Norbert Knarr, Antje Rothmund & Markus Stroppel

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  1. Norbert Knarr
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  2. Antje Rothmund
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  3. Markus Stroppel
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Correspondence to Markus Stroppel.

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Knarr, N., Rothmund, A. & Stroppel, M. Linearly small elation quadrangles. J. Geom. 95, 49–67 (2009). https://doi.org/10.1007/s00022-009-0017-3

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