Switching of generalized quadrangles of order s and applications
نویسنده
چکیده
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 {*}) U {«}) with xeO can be obtained by switching from T2(O). Applications to translation generalized quadrangles of order s, s even, and generalized quadrangles of order (s,s), s even, satisfying Property (G), are given.
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