A coordinatization of generalized quadrangles of order (s, s + 2)
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...
متن کاملSwitching of generalized quadrangles of order s and applications
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 {*}) ...
متن کاملS ep 2 00 7 Elation generalised quadrangles of order ( s , p ) , where p is prime
We show that an elation generalised quadrangle which has p + 1 lines on each point, for some prime p, is classical or arises from a flock of a quadratic cone (i.e., is a flock quadrangle).
متن کاملSome notes on generalized quadrangles of order s with a span of regular points
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...
متن کاملCoordinatization structures for generalized quadrangles and glued near hexagons
A generalized admissible triple is a triple T = (L, X,∆), where X is a set of size s + 1 ≥ 2, L is a Steiner system S(2, s + 1, st + 1), t ≥ 1, with point-set P and ∆ is a very nice map from P × P to the group Sym(X) of all permutations of the set X. Generalized admissible triples can be used to coordinatize generalized quadrangles with a regular spread and glued near hexagons. The idea of coor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1988
ISSN: 0097-3165
DOI: 10.1016/0097-3165(88)90070-2