交错群与旗传递点本原非对称2-（v，k，3）设计

受旗传递2-(v,k,3)对称设计和非对称2-(v,k,2)设计有关分类结果的启发,本论文继续研究旗传递非对称2-(v,k,3)设计.文章利用置换群的理论和组合设计的数量性质,借助计算机代数软件Gap和Magma,完全分类了自同构群G旗传递点本原,且基柱Soc(G)为交错群An(n≥5)的非对称2-(v,k,3)设计,证明了此类设计只能是唯一的2-(5,3,3)设计,且G=A_5或S_5.     

^2F4（q2）与2-（v，k，3）对称设计

本文要证明不存在一个非平凡2-（v，k，3）对称设计，它的旗传递自同构群的基柱是^2F4（q2）     

Suzuki群与Steiner 4设计

本文研究了非平凡Steiner 4设计的自同构群是旗传递的情形.利用有限2传递置换群的分类,得到了旗传递非平凡Steiner 4设计的自同构群的基柱不是Suzuki群.     

关于可解区组传递的2-(56,7,1)设计

设G是设计2-(5~6,7,1)的一个可解区传递自同构群,则G是旗传递的且G■A■L(1,5~6)．     

自同构群基柱为~3D_4(q)的2-(v,k,1)设计

2-(v,k,1)设计的存在性问题是组合设计理论中重要的问题,当这类设计具有一个有意义自同构群时,讨论其存在性是尤其令人感兴趣的.30年前,一个6人团队基本上完成了旗传递的2-(v,k,1)设计分类.此后,人们开始致力于研究区传递但非旗传递的2-(v,k,1)设计的分类课题.本文证明了自同构群基柱为~3D_4(q)的区传递及点本原非旗传递的2-(v,k,1)设计是不存在的.     

以$M_{11}$为基柱的旗传递点本原2-设计的完全分类

近年来,很多学者研究了以散在单群作为本原自同构群基柱的旗传递2-设计的一些分类工作.本文在此基础之上,给出了以散在单群$M_{11}$作为基柱的旗传递点本原2-设计的完全分类,得到了14个不同构的非平凡2-设计.     

旗传递5-(v,k,2)设计的分类

本文研究了5-(v,k,2)设计的分类问题.利用典型群PSL(2,q)的子群作用于投影线的轨道定理,证明了旗传递5-(v,k,2)设计的自同构群的基柱不能与PSL(2,3n)同构.从而证明了不存在旗传递的5-(v,k,2)设计.     

Steiner 5-设计上的Camina-Gagen定理

著名的Camina-Gagen定理表明,若群G是一个满足k整除v的2-(v, k, 1)设计的区传递的自同构群,则G是旗传递的.本文将这个定理推广到5-(v, k, 1)设计上,并证明了如果群G区传递地作用在一个非平凡的5-(v, k, 1)设计上且满足k整除v,则G是旗传递的.     

区传递的2-（v，k，1）设计与射影辛群PSpn（q）

分类自同构群为射影辛群PSpn(q)的区传递2-(v,k,1)设计,得到如下定理:设D为一个2-(v,k,1)设计,G≤Aut(D)是区传递,点本原但非旗传递的.若q为偶数且n≥14,则GPSpn(q).     

区传递的2-（v，k，1）设计与李型单群E8（q）

分类自同构群的基柱为李型单群E8（q）的区传递2-（v，k，1）设计，得到如下定理：设D为一个2-（v，k，1）设计，G≤Aut（D）是区传递、点本原但非旗传递的．若q〉24√（krk-kr＋1）f（这里kr=（k，v-1），q=p^f，p是素数，f是正整数），则Soc（G）≌／E8（q）．     

搜索区传递2-（q，4，1）设计

对于区传递但非旗传递的可解2-（q，4，1）设计，Camina指出，当q=13，37，61，109，157，181时有具体的例子，但是否有更多的q产生具体例子有待研究。主要结果：设q是素数幂且q=13（mod24），则对于每个q〈2000，总存在区传递但非旗传递的2-（q，4，1）设计。     

On 2-(45, 12, 3) designs

Under the assumption that the incidence matrix of a 2-(45, 12, 3) design has a certain block structure, we determine completely the number of nonisomorphic designs involved. We discover 1136 such designs with trivial automorphism group. In addition we analyze all 2-(45, 12, 3) designs having an automorphism of order 5 or 11. Altogether, the total number of nonisomorphic 2-(45, 12, 3) designs found in 3752. Many of these designs are self-dual and each of these self-dual designs possess a polarity. Some have polarities with no absolute points, giving rise to strongly regular (45, 12, 3, 3) graphs. In total we discovered 58 pairwise nonisomorphic strongly regular graphs, one of which has a trivial automorphism group. Further, we analyzed completely all the designs for subdesigns with parameters 2-(12, 4, 3), 2-(9, 3, 3), and 2-(5, 4, 3). In the first case, the number of 2-(12, 4, 3) subdesigns that a design possessed, if non-zero, turned out to be a multiple of 3, whereas 2-(9, 3, 3) subdesigns were so abundant it was more unusual to find a design without them. Finally, in the case of 2-(5, 4, 3) subdesigns there is a design, unique amongst the ones discovered, that has precisely 9 such subdesigns and these form a partition of the point set of the design. This design has a transitive group of automorphisms of order 360. © 1996 John Wiley & Sons, Inc.     

马休群与斯坦诺5设计

讨论了马体群旗传递作用于斯坦诺5设计上的情况，得到了如下结论：设D=（X，Ω，I）是非平凡的斯坦诺5设计，D的自同构群G旗传递地作用在D上。若G是几乎单群，则 （i）基柱Soc（G）不是下列单群：N=Mv，v=11，22，23和N=M11,v=12 （ii）若N=M12，v=12，则D是一个5-（12，6，1）设计，且G M12 （iii）若N=M24，v=24，则D是一个5-（24，8，1）设计，且G M24。     

The 2-(9, 4, 3) and 3-(10, 5, 3) designs

It is shown that there is a unique 2-(9, 4, 3) design with three different extensions to a 3-(10, 5, 3) design. Two of the extensions are isomorphic and have a further extension to the unique 4-(11, 6, 3) design. There is another 2-(9, 4, 3) design with just two extensions to a 3-design. There are 11 2-(9, 4, 3) designs in all, as announced by van Lint, et al. and Stanton et al. There are seven 3-(10, 5, 3) designs of which one is triply transitive, another transitive, and the rest are not transitive but are self-complementary. The transitive 3-designs each have one restriction to a 2-design. Of the non-transitive 3-designs 4 each have two restrictions and the fifth has three.     

Dimensional linear spaces whose automorphism group is (line,hyperplane)-flag transitive

We classify the pairs (S, G) where S is a finite n-dimensional linear space with n 4 and G is an automorphism group of S acting transitively on the (line, hyperplane)-flags. We show in particular that S must be either a Desarguesian projective or affine space provided with its subspaces of dimension n - 1, or a Mathieu-Witt design provided with its blocks and its subsets of size n - 1. Our proof uses a recent classification of the flag transitive 2-(v, k, 1) designs, which in turn heavily depends on the classification of all finite simple groups. The case n = 3 has been settled in another paper.     

Flag-Transitive 3-(v,k, 3) Designs and PSL(2, q) Groups

This article is a contribution to the study of the automorphism groups of 3-(v,k,3) designs.Let S =(P,B) be a non-trivial 3-(q+ 1,k,3) design.If a two-dimensional projective linear group PSL(2,q) acts flag-transitively on S,then S is a 3-(q + 1,4,3) or 3-(q + 1,5,3) design.     

A classification of flag‐transitive point‐imprimitive 2‐designs with block size 6

We determine all 2‐ designs admitting a flag‐transitive point‐imprimitive automorphism group.     

马休群与斯坦诺4-设计

讨论了马休群旗传递作用于斯坦诺4-设计上情况,得到了如下结论：设D=（X,B,I）是非平凡的斯坦诺4-设计,D的自同构群G旗传递地作用在D上。若G是几乎单群,则 i）Soc（G）不同构于单群：N=Mv,v=12,22,24和N=M11,v=12; ii）若N=M11,v=11,则D是一个斯坦诺4-（11,5,1）设计,且G△M11; iii）若N=M23,v=23,则D是一个斯坦诺4-（23,7,1）设计,且G△M23。