Primitive flag-transitive generalized hexagons and octagons

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Primitive flag-transitive generalized hexagons and octagons

Suppose that an automorphism group G acts flag-transitively on a finite generalized hexagon or octagon S, and suppose that the action on both the point and line set is primitive. We show that G is an almost simple group of Lie type, that is, the socle of G is a simple Chevalley group.

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One-point extensions of generalized hexagons and octagons

In this note, we prove the uniqueness of the one-point extension S of a generalized hexagon of order 2 and prove the non-existence of such an extension S of any other finite generalized hexagon of classical order, different from the one of order 2, and of the known finite generalized octagons provided the following property holds: for any three points x, y and z of S, the graph theoretic distan...

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Flag-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).

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Flag-transitive point-primitive $(v,k,4)$ symmetric designs with exceptional socle of Lie type

Let $G$ be an automorphism group of a‎ ‎$2$-$(v,k,4)$ symmetric design $mathcal D$‎. ‎In this paper‎, ‎we‎ ‎prove that if $G$ is flag-transitive point-primitive‎, ‎then the‎ ‎socle of $G$ cannot be an exceptional group of Lie type‎.

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Reduction for primitive flag-transitive (v, k, 4)-symmetric designs

It has been shown that if a (v,k,λ )-symmetric design with λ ≤ 3 admits a flag-transitive automorphism group G which acts primitively on points, then G must be of affine or almost simple type. Here we extend the result to λ = 4.

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ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series A

سال: 2008

ISSN: 0097-3165

DOI: 10.1016/j.jcta.2008.02.004