Block-Transitive 4-(v,k,4) Designs and Ree Groups

This article is a contribution to the study of the automorphism groups of designs. Let be a non-trivial design where for some positive integer , and is block-transitive. If the socle of G is isomorphic to the simple groups of lie type, then G is not flag-transitive.

On Soluble Block-Transitive 2-(5~6,7,1)Designs

Let G be a soluble block-transitive automorphism group of 2-（5^6, 7, 1） design D. Then G is flag-transitive or G ≤ AΓL（1, 5^6）.

Block-Transitive 2-(v,k,1) Designs and Groups E_6(q)

This article is a contribution to the study of block-transitive automorphism groups of 2-（v,k,1） block designs. Let D be a 2-（v,k,1） design admitting a block-transitive, pointprimitive but not flag-transitive automorphism group G. Let kr = （k,v-1） and q = pf for prime p. In this paper we prove that if G and D are as above and q （3（krk-kr ＋ 1）f）1/3, then G does not admit a simple group E6（q） as its socle.

On Block-transitive 6-（v, k, λ）-Designs with k at Most 10000

In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.

The Group of Automorphisms of Transitive 2-(v, 23, 1) Designs

This paper is a contribution to the study of the automorphism groups of 2 - （v, k, 1） designs. Let D be a 2 - （v, 23, 1） design and G a block-transitive and point-primitive group of automorphism of D. Then the socle of G is not Sz（q） and 2G2（q）.