منابع مشابه
Generalised Polygons Admitting a Point-Primitive Almost Simple Group of Suzuki or Ree Type
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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After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.
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Let (P ,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = ⋃ x∈X{y : yIx} and by [X ] = (X)I ∪ X . With this terminology a partial linear space (P ,L, I) is said to admit a (1,≤ k)-identifying code if and only if the sets [X ] are mutually different for all X ⊆ P ∪L with |X | ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)...
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Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with kernel F and complement H. In the case where G is a finite p-group such that G = [G,F ] it is proved that the order of G is bounded above in terms of the order of H and the order of the fixed-point subgroup CG(H) of the complement, and the rank of G is bounded above in terms of |H| and the rank of C...
متن کاملThe Norm of a Ree Group
We give an explicit construction of the Ree groups of type G2 as groups acting on mixed Moufang hexagons together with detailed proofs of the basic properties of these groups contained in the two fundamental papers of Tits on this subject, [7] and [8]. We also give a short proof that the norm of a Ree group is anisotropic.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2004
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2003.10.001