| 区传递的$2-(v, k, 1)$ 设计与单群$E_6(q)$ |
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| 引用本文： | 韩广国.区传递的$2-(v, k, 1)$ 设计与单群$E_6(q)$[J].数学研究及应用,2010,30(4):581-588. |
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| 作者姓名： | 韩广国 |
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| 作者单位： | 杭州电子科技大学数学研究所, 浙江 杭州 310018; 解放军信息工程大学信息工程学院, 河南 郑州 450002 |
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| 基金项目： | 国家自然科学基金(Grant No.10871205),中国博士后基金(Grant No.20080441323),浙江省教育厅项目(Grant No.Y200804780). |
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| 摘 要： | 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.
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| 关 键 词： | block design block-transitive point-primitive automorphism group. |
| 收稿时间： | 2008/11/11 0:00:00 |
| 修稿时间： | 2009/5/15 0:00:00 |
Block-Transitive $2$-$(v,k,1)$ Designs and Groups $E_6(q)$ |
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| Guang Guo HAN.Block-Transitive $2$-$(v,k,1)$ Designs and Groups $E_6(q)$[J].Journal of Mathematical Research with Applications,2010,30(4):581-588. |
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| Authors: | Guang Guo HAN |
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| Institution: | Institute of Mathematics, Hangzhou Dianzi University, Zhejiang 310018, P. R. China;Institute of Information Engineering, Information Engineering University, Henan 450002, P. R. China |
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| Abstract: | This article is a contribution to the study of block-transitive automorphism groups of $2$-$(v, k, 1)$ block designs. Let ${\cal D}$ be a $2$-$(v, k, 1)$ design admitting a block-transitive, point-primitive but not flag-transitive automorphism group $G$. Let $k_r=(k,v-1)$ and $q=p^f$ for prime $p$. In this paper we prove that if $G$ and ${\cal D}$ are as above and $q>$ $(3(k_rk-k_r+1)f)^{1/3}$, then $G$ does not admit a simple group $E_6(q)$ as its socle. |
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| Keywords: | block design block-transitive point-primitive automorphism group |
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