Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

自同构群包含有限单群的代数或组合结构的研究

• 批准号: 19340002
• 负责人: KITAZUME Masaaki
• 金额: $ 6.66万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340002/
• 关键词: 有限群; 符号; デザイン; グラフ; 単純群; 散在型単純群; 格子; 頂点作用素代数

We have studied some algebraic structures and combinatorial structured whose automorphism groups contain finite simple groups.(1) We have studied the binary code spanned by the sets of fixed points of the involutions of a finite transitive permutation group and its dual code. New self-dual codes invariant under the Hall-Janko group and the Rudvalis group have been constructed, respectively.(2) We have studied rank 3 graphs related to some sporadic simple groups (especially, HJ, Suz, M24). New constructions of these rank 3 graphs from some designs have been obtained.(3) We have determined the minimum value m such that a given Niemeier lattice is a m-neighbor of the Leech lattice.

我们研究了自同构群包含有限单群的代数结构和组合结构。(1)研究了有限传递置换群的对合不动点集所生成的二元码及其对偶码。分别在Hall-Janko群和Rudvalis群下构造了新的自对偶码不变量。(2)研究了一些零星单群(特别是HJ，Suz，M24)的秩3图。(3)确定了一个给定的Niemeier格是Leech格的m-邻域的最小值m。

项目成果

On the maximum coclique of the rank 3 graph of 2^<11>:M_<24>

关于2^<11>的三阶图的最大尾花：M_<24>

• 发表时间: 2009
• 期刊: Journal of Combinatorial Designs 17
• 作者: N.Horiguchi;M.Kitazume;H.Nakasora
• 通讯作者: H.Nakasora

A construction of the sporadic Suzuki graph from U_3(4)

U_3(4) 的零星 Suzuki 图的构造

• 发表时间: 2009
• 期刊: Journal of Combinatorial Theory (A) 116
• 作者: A.E.Brouwer;N.Horiguchi;M.Kitazume;H.Nakasora
• 通讯作者: H.Nakasora

Co 3をめぐって

关于Co 3

• 发表时间: 2011
• 作者: N. Horiguchi;M. Kitazume;H. Nakasora;北詰正顕
• 通讯作者: 北詰正顕

Neighbors of the Leech lattice

水蛭格子的邻居

• 发表时间: 2010
• 作者: N. Horiguchi;M. Kitazume;H. Nakasora;北詰正顕;北詰正顕;北詰正顕
• 通讯作者: 北詰正顕

On the maximum coclique of the rank 3 graph of 211. M24

211.M24 的三阶图的最大尾翼

• 期刊: Journal of Combinatorial Designs (印刷中)
• 作者: N. Horiguchi;M. Kitazume;H. Nakasora
• 通讯作者: H. Nakasora