Block Primitive 2- (v, k, 1) Designs Admitting a Ree Simple Group
نویسندگان
چکیده
منابع مشابه
Existence of 2-(v, k, 1) Designs Admitting a Block-Transitive Group of Affine Type
In this paper we use Weil’s estimate on character sums to prove that large admissible prime powers q admit 2-(q, k, 1) designs having block-transitive automorphism groups in AGL(1, q).
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Let G be a collineation group of a thick finite generalised hexagon or generalised octagon Γ. If G acts primitively on the points of Γ, then a recent result of Bamberg et al. shows that G must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup S of G cannot be a Suzuki group or a Ree group of type G2, and that if S is a Ree group of type F4, then Γ is ...
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A 2&(v, k, 1) design D=(P, L) is a system consisting of a finite set P of v points and a collection L of a k-subset of P, called lines, such that each 2-subset of P is contained in precisely one line. We shall always assume that 2<k<v. Let G Aut(D) be a group of automorphisms of a 2&(v, k, 1) design D. The group G is said to be line-transitive (line-primitive, respectively) on D if G is transit...
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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.
متن کاملDoubly homogeneous 2-(v, k, 1) designs
A 2-(v, k, 1) design 9 = (S, 93) is a finite set S of u points and a collection $3 of k-subsets of S, called blocks, such that any 2-subset of S is contained in precisely one block. We will always assume that 2 <k < o. Let G d Aut 9 be a group of automorphisms of a 2-(u, k, 1) design 9. Those designs $3 for which G acts doubly transitively on the points have been classified by Kantor [6] and, f...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2002
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0616