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| 旗传递5-(v,k,2)设计的分类 |
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龚罗中1, 刘伟俊2, 唐剑雄2, 谭琼华3
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1.湖南科技学院计算数学研究所, 湖南 永州 425199;2.中南大学数学与统计学院, 湖南 长沙 410075;3.南华大学数理学院, 湖南 衡阳 421001
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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. |
| 关键词: t-设计 旗传递 区组设计 自同构群 |
| DOI： |
| 分类号:O157.2;O152.8 |
| 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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| CLASSIFICATION OF FLAG-TRANSITIVE 5-(v,k,2) DESIGNS |
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GONG Luo-zhong1, LIU Wei-jun2, TANG Jian-xiong2, TAN Qiong-hua3
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1.Institute for Computational Mathematics, Hunan University of Science and Engineering, Yongzhou 425199, China;2.School of Mathematics and Statistics, Central South University, Changsha 410075, China;3.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. |
| Key words: t-designs flag-transitive block-design automorphisms |
