On primitivity and reduction for flag-transitive symmetric designs

نویسنده

  • Eugenia O'Reilly Regueiro
چکیده

We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a biplane admits a primitive, flag-transitive automorphism group of affine type.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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).

متن کامل

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.

متن کامل

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.

متن کامل

Flag-transitive non-symmetric 2-designs with (r, λ) = 1 and alternating socle

This paper deals with flag-transitive non-symmetric 2-designs with (r, λ) = 1. We prove that if D is a non-trivial non-symmetric 2-(v, k, λ) design with (r, λ) = 1 and G 6 Aut(D) is flag-transitive with Soc(G) = An for n > 5, then D is a 2-(6, 3, 2) design, the projective space PG(3, 2), or a 2-(10, 6, 5) design.

متن کامل

A census of highly symmetric combinatorial designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v, k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have rema...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 109  شماره 

صفحات  -

تاریخ انتشار 2005