共查询到17条相似文献,搜索用时 234 毫秒
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韩广国 《高校应用数学学报(A辑)》2011,26(1):78-88
讨论区传递的2-(v,k,1)设计的分类问题.特别地,讨论自同构群的基柱为典型单群的区传递,点本原但非旗传递的2-(v,9,1)设计.设D为一个2-(v,9,1)设计,若G≤Aut(D)是区传递,点本原但非旗传递的,则G的基柱Soc(G)不是有限域GF(q)上的典型单群.结合Camina,Praeger,刘伟俊,李慧陵... 相似文献
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三平面也称为2-(v,k,3)对称设计.设D是一个三平面,且G是D的全自同构群Aut(D)的一个子群.本文证明了若G是旗传递和点本原的,则G的基柱不可能是例外Lie型单群. 相似文献
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李上钊 《数学年刊A辑(中文版)》2017,38(3):289-294
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. 相似文献
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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. 相似文献
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区传递的2-(ν,κ,1)设计与李型单群E8(q) 总被引:1,自引:1,他引:0
韩广国 《高校应用数学学报(A辑)》2007,22(4)
分类自同构群的基柱为李型单群E8(q)的区传递2-(ν,κ,1)设计,得到如下定理:设D为一个2-(ν,κ,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=pf,p是素数,f是正整数),则Soc(G)(≠)E8(q). 相似文献
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本文研究了基柱同构于2F4(q)的线传递的几乎单群.利用了有限线性空间上线传递的自同构群的经典结论,以及2F4(q)的阶和极大子群等性质,获得了点稳定子群和线稳定子群的分类. 相似文献
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韩广国 《高校应用数学学报(A辑)》2007,22(4):483-490
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). 相似文献
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若$\cal D$为一个非平凡旗传递点本原对称$(v,k,4)$设计, 其基柱为${\rm PSL}_n(q)$且$G\leq {\rm Aut}(\cal D)$. 那么, $\cal D$ 必为$2$-$(15,8,4)$设计且${\rm Soc}(G)={\rm PSL}_2(9)$. 相似文献
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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. 相似文献
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Let D be a triplane, i.e., a 2-(v,k,3) symmetric design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G is flag-transitive point-primitive, then the socle of G cannot be a sporadic simple group. 相似文献
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A triplane is a ( v, k, 3)-symmetric design. Let G be a subgroup of the full automorphism group of a triplane D. In this paper we prove that if G is flag-transitive and point-primitive, then the socle of G cannot be a simple exceptional group of Lie type. 相似文献
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《数学季刊》2015,(4)
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 ~2G_2(q).Key words: block-transitive; point-primitive; design; socle 相似文献
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Michael Huber 《Journal of Algebraic Combinatorics》2007,26(2):183-207
Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural
one. Consequently, in the last decades flag-transitive Steinert-designs (i.e. flag-transitive t-(v,k,1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been
possible in recent years to essentially characterize all flag-transitive Steiner 2-designs. However, despite the finite simple
group classification, for Steiner t-designs with parameters t > 2 such characterizations have remained challenging open problems for about 40 years (cf. [11, p. 147] and [12 p. 273],
but presumably dating back to around 1965). The object of the present paper is to give a complete classification of all flag-transitive
Steiner 4-designs. Our result relies on the classification of the finite doubly transitive permutation groups and is a continuation
of the author's work [20, 21] on the classification of all flag-transitive Steiner 3-designs.
2000 Mathematics Subject Classification. Primary 51E10 . Secondary 05B05 . 20B25 相似文献
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Designs, Codes and Cryptography - In this paper, we study the flag-transitive automorphism groups of 2-designs and prove that if G is a flag-transitive automorphism group of a 2-design $$\mathcal... 相似文献