| 旗传递5-(v,k,2)设计的分类 |
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| 引用本文： | 龚罗中,刘伟俊,唐剑雄,谭琼华. 旗传递5-(v,k,2)设计的分类[J]. 数学杂志, 2014, 34(3): 553-561 |
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| 作者姓名： | 龚罗中 刘伟俊 唐剑雄 谭琼华 |
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| 作者单位： | 湖南科技学院计算数学研究所;中南大学数学与统计学院;南华大学数理学院; |
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| 基金项目： | 国家自然科学基金资助(11271208);湖南省教育厅科研基金资助(12B050);湖南科技学院重点学科建设项目资助 |
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| 摘 要： | 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.
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| 关 键 词： | t-设计 旗传递 区组设计 自同构群 |
| 收稿时间： | 2013-08-10 |
| 修稿时间： | 2013-12-17 |
CLASSIFICATION OF FLAG-TRANSITIVE 5-(v,k,2) DESIGNS |
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| GONG Luo-zhong,LIU Wei-jun,TANG Jian-xiong and TAN Qiong-hua. CLASSIFICATION OF FLAG-TRANSITIVE 5-(v,k,2) DESIGNS[J]. Journal of Mathematics, 2014, 34(3): 553-561 |
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| Authors: | GONG Luo-zhong LIU Wei-jun TANG Jian-xiong TAN Qiong-hua |
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| Affiliation: | Institute for Computational Mathematics, Hunan University of Science and Engineering, Yongzhou 425199, China,School of Mathematics and Statistics, Central South University, Changsha 410075, China,School of Mathematics and Statistics, Central South University, Changsha 410075, China and School of Mathematics and Physics, University of South China, Hengyang 421001, China |
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| Abstract: | This paper is devoted to the classiflcation of flag-transitive 5-designs. Using the orbital theorem of classical simple group PSL(2,q), it is proved that the socle of the flag-transitively act automorphisms of a non-trivial 5-(v,k,2) designs can not be isomorphic to PSL(2,3n), and it is proved that there exist not non-trivial 5-(v,k,2)designs. |
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| Keywords: | t-designs flag-transitive block-design automorphisms |
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