Symmetric Designs from the G2(q) Generalized Hexagons
نویسندگان
چکیده
We describe symmetric designs D with classical parameters v=(q 6 − 1)/(q − 1), k=(q 5 − 1)/(q − 1), l=(q 4 − 1)/(q − 1), and automorphism group Aut(G 2 (q)).
منابع مشابه
I Journal of Geometry Some Combinatorial and Geometric Characterizations of the Finite Dual Classical Generalized Hexagons
We characterize the dual of the generalized hexagons naturally associated to the groups G2(q) and 3D4(q) by looking at certain configurations, and also by considering intersections of traces. For instance, the dual of a generalized hexagon F of finite order (s, t) is associated to the Chevaliey groups mentioned above if and only if the intersection of any two traces x v and x z, with some addit...
متن کاملFlag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
متن کاملExtended Generalized Hexagons and the Suzuki Chain
Four extended generalized hexagons related to the simple groups G2(2)', PSU4(3), HJ and Suz are characterized by the condition that any triple of points {x, y, z) is a clique of the point graph not in a circle of the extended hexagon if and only if the distance of y and z in the residue at x is 3.
متن کاملA Characterization of the Finite Moufang Hexagons by Generalized Homologies
A generalized homology of a generalized hexagon 5^ is an auto-morphism of S? fixing all points on two mutually opposite lines or fixing all lines through two mutually opposite points. We show that if 5? is finite and if it admits "many" generalized homologies, then 5? is Moufang and hence classical. 1. Introduction and notation, A (finite thick) generalized hexagon of order (s, t) is a point-li...
متن کاملSome Applications of Magma in Designs and Codes: Oval Designs, Hermitian Unitals and Generalized Reed-Muller Codes
We describe three applications of Magma to problems in the area of designs and the associated codes: • Steiner systems, Hadamard designs and symmetric designs arising from a oval in an even order plane, leading in the classical case to bent functions and difference-set designs; • the hermitian unital as a 2-(q + 1, q + 1, 1) design, and the code over Fp where p divides q + 1; • a basis of minim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 98 شماره
صفحات -
تاریخ انتشار 2002