On 2-designs Whose Group of Automorphisms Is Transitive on the Ordered Pairs of Intersecting Lines
نویسنده
چکیده
THEOREM 1. Let G be a permutation group on a finite set S of v points. If a, b are distinct points then the set ab of all points fixed by the stabilizer Gab will be called aline. Assume that (i) G is 2-transitive on the points of S; (ii) the number k of points on the line ab satisfies 2 < k < v; (iii) Gab is transitive on the lines containing a and distinct from ab. Then S provided with the set of lines is an affine space AG(d, q) of dimension d^lon some field oforderq ^ 3 or Sis a projective space PG(d, 2) of dimension d ^ 2 and order 2.
منابع مشابه
Unitary graphs and classification of a family of symmetric graphs with complete quotients
A finite graph Γ is called G-symmetric if G is a group of automorphisms of Γ which is transitive on the set of ordered pairs of adjacent vertices of Γ. We study a family of symmetric graphs, called the unitary graphs, whose vertices are flags of the Hermitian unital and whose adjacency relations are determined by certain elements of the underlying finite fields. Such graphs admit the unitary gr...
متن کاملSharply $(n-2)$-transitive Sets of Permutations
Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...
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 کاملON ABSOLUTE CENTRAL AUTOMORPHISMS FIXING THE CENTER ELEMENTWISE
Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. In this paper we give necessary and sufficient condition on G such that each absolute central automorphism of G fixes the centre element-wise. Also we classify all groups of orders p^3 and p^4 whose absolute central automorphisms fix the centre element-wise.
متن کاملFlag-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.
متن کامل