| 李上钊.自同构群基柱为3D_4(q)的2-(v, k, 1)设计[J].数学年刊A辑,2017,38(3):289~294 |
| 自同构群基柱为3D_4(q)的2-(v, k, 1)设计 |
| On the 2-(v, k, 1) Designs Admitting Automorphism Groups with Socle 3D_4(q) |
| Received:May 17, 2015 Revised:June 02, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0024 |
| 中文关键词: Block-transitive, Point-primitive, Design, Automorphism |
| 英文关键词:Block-transitive, Point-primitive, Design, Automorphism |
| 基金项目:本文受到国家自然科学基金(No.11471054,No.11671402,No.11301377),江苏省自然科学基金(No.BK20161265,No.BK20170433),江苏省高校自然科学基金(No.16KJB110001),江苏省普通高校学术学位研究生科研创新计划项目(No.KYLX1213)和常熟理工学院科研项目(No.QZ1507)的资助. |
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| 中文摘要: |
| $2-(v, k, 1)$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. |
| 英文摘要: |
| One of the outstanding problems in combinatorial design theory
concerns the existence of $2-(v, k, 1)$ designs. In particular, the
existence of $2-(v, k, 1)$ designs admitting an interesting group of
automorphisms is of great interest. Thirty years ago, a six-person
team classified $2-(v, k, 1)$ designs which have flag-transitive
automorphism groups. Since then, the effort has been to classify
those $2-(v, k, 1)$ designs which are block-transitive but not
flag-transitive. In this paper the author proves the nonexistence of
$2-(v, k, 1)$ designs admitting a block-transitive and
point-primitive but not flag-transitive automorphism group $G$ with
socle $^3D_4(q)$. |
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