Generalized Quadrangles of Order (s, s2), III
نویسندگان
چکیده
منابع مشابه
Classification of span-symmetric generalized quadrangles of order s
A line L of a finite generalized quadrangle S of order ðs; tÞ, s; t > 1, is an axis of symmetry if there is a group of full size s of collineations of S fixing any line which meets L. If S has two non-concurrent axes of symmetry, then S is called a span-symmetric generalized quadrangle. We prove the twenty-year-old conjecture that every span-symmetric generalized quadrangle of order ðs; sÞ is c...
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Let & = (P, £, I) be a generalized quadrangle of order 5, s φ 1, having a flag (x, L) with χ and L regular. Then a generalized quadrangle SP = (Ρ',Β',Ι') of order s can be constructed. We say that &" is obtained by switching from & with respect to (je, L). Examples are given where ¥ £ &'\ e.g., starting from a T2(O) of Tits, with O an oval of PG(2, q), q even, with nucleus «, the GQ T2((O {*}) ...
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Let Q be a generalized quadrangle of order s with a regular point x. The set x⊥ together with all spans which are contained in x⊥ define a projective plane of order s. We introduce a property (Py) for every point y of Q noncollinear with x and prove that this property is equivalent with the regularity of the point y. We will use this to give an elementary proof for the following result: every g...
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A generalized quadrangle of order s ≥ 2 is isomorphic to W (s) if and only if there is a hyperbolic line every point of which is regular. This is a characterization of the symplectic generalized quadrangle W (s) which only needs the existence of s + 1 regular points (in a nice position).
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1999
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2959