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• W2479483281 startingPage "429" @default.
• W2479483281 abstract "Modulo a combination of duality, translation duality or Payne integration, every known finite generalized quadrangle except for the Hermitian quadrangles $$mathcal {H}(4,q^2)$$ , is an elation generalized quadrangle for which the elation point is a center of symmetry—that is, is a “skew translation generalized quadrangle” (STGQ). In this series of papers, we classify and characterize STGQs. In the first installment of the series, (1) we obtain the rather surprising result that any skew translation quadrangle of finite odd order (s, s) is a symplectic quadrangle; (2) we determine all finite skew translation quadrangles with distinct elation groups (a problem posed by Payne in a less general setting); (3) we develop a structure theory for root elations of skew translation quadrangles which will also be used in further parts, and which essentially tells us that a very general class of skew translation quadrangles admits the theoretical maximal number of root elations for each member, and hence, all members are “central” (the main property needed to control STGQs, as which will be shown throughout); and (4) we show that finite “generic STGQs,” a class of STGQs which generalizes the class of the previous item (but does not contain it by definition), have the expected parameters. We conjecture that the classes of (3) and (4) contain all STGQs." @default.
• W2479483281 created "2016-08-23" @default.
• W2479483281 creator A5012344209 @default.
• W2479483281 date "2017-12-04" @default.
• W2479483281 modified "2023-09-25" @default.
• W2479483281 title "Central aspects of skew translation quadrangles, 1" @default.
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• W2479483281 doi "https://doi.org/10.1007/s10801-017-0801-3" @default.
• W2479483281 hasPublicationYear "2017" @default.
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